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  <div class="header-title">Product Rule of Logarithms Derivation</div>

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      <div class="badge">1</div>
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          <span class="card-label">1. Define Variables</span>
          <span class="card-desc">Exponential &hArr; Log form</span>
        </div>
        <div class="math-row">
          <span><i>M</i> = <i>b</i><sup><i>x</i></sup> &hArr; <i>x</i> = log<sub><i>b</i></sub>(<i>M</i>)</span>
          <span style="color:#64748b; margin: 0 2px;">and</span>
          <span><i>N</i> = <i>b</i><sup><i>y</i></sup> &hArr; <i>y</i> = log<sub><i>b</i></sub>(<i>N</i>)</span>
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          <span class="card-label">2. Multiply Expressions</span>
          <span class="card-desc">Exponent product rule</span>
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          <span><i>M</i><i>N</i> = <i>b</i><sup><i>x</i></sup> &middot; <i>b</i><sup><i>y</i></sup> = <span class="math-highlight"><i>b</i><sup><i>x</i> + <i>y</i></sup></span></span>
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          <span>log<sub><i>b</i></sub>(<i>M</i><i>N</i>) = log<sub><i>b</i></sub>(<i>b</i><sup><i>x</i> + <i>y</i></sup>) = <span class="math-highlight"><i>x</i> + <i>y</i></span></span>
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      <div class="badge">4</div>
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          <span class="card-desc">Replace <i>x</i> and <i>y</i></span>
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          <span class="math-highlight">log<sub><i>b</i></sub>(<i>M</i><i>N</i>) = log<sub><i>b</i></sub>(<i>M</i>) + log<sub><i>b</i></sub>(<i>N</i>)</span>
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Laws of Logarithms: Product, Quotient and Power

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<body>

  
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      <span class="tag tag-exp">Exponent Law</span>
      <div class="math-eq math-font">
        <span class="frac">
          <span class="frac-num"><span class="math-var">b</span><sup><span class="math-var">u</span></sup></span>
          <span class="frac-den"><span class="math-var">b</span><sup><span class="math-var">v</span></sup></span>
        </span>
        <span>=</span>
        <span><span class="math-var">b</span><sup><span class="math-var">u</span>&minus;<span class="math-var">v</span></sup></span>
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    <div class="bridge-arrow">⟷</div>

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      <span class="tag tag-log">Quotient Rule</span>
      <div class="math-eq math-font">
        <span>log<sub><span class="math-var">b</span></sub></span>
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          <span class="paren-sym">(</span>
          <span class="frac">
            <span class="frac-num"><span class="math-var">x</span></span>
            <span class="frac-den"><span class="math-var">y</span></span>
          </span>
          <span class="paren-sym">)</span>
        </div>
        <span>=</span>
        <span>log<sub><span class="math-var">b</span></sub><span class="math-var">x</span> &minus; log<sub><span class="math-var">b</span></sub><span class="math-var">y</span></span>
      </div>
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      document.getElementById('playBtn').textContent = isPlaying ? '⏸' : '▶';
      if (isPlaying) {
        startTimer();
      } else {
        clearInterval(timer);
      }
    }

    function startTimer() {
      clearInterval(timer);
      timer = setInterval(() => {
        if (isPlaying) nextStep();
      }, 3200);
    }

    window.addEventListener('DOMContentLoaded', () => {
      renderStep();
      startTimer();
    });
  </script>
</body>
</html>

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <style>
    * { 
      box-sizing: border-box; 
      margin: 0; 
      padding: 0; 
    }

    body {
      font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif;
      background: transparent;
      color: #0f172a;
      padding: 10px;
      line-height: 1.4;
      -webkit-font-smoothing: antialiased;
    }

    .container {
      display: grid;
      grid-template-columns: 1fr 1fr;
      gap: 12px;
      width: 100%;
      max-width: 760px;
      margin: 0 auto;
    }

    @media (max-width: 580px) {
      .container {
        grid-template-columns: 1fr;
        gap: 14px;
      }
    }

    /* Column Panels */
    .column {
      display: flex;
      flex-direction: column;
      gap: 10px;
    }

    /* Headers */
    .panel-header {
      display: flex;
      align-items: center;
      justify-content: space-between;
      padding: 4px 2px 8px;
      border-bottom: 2px solid;
    }

    .column-correct .panel-header {
      border-color: #16a34a;
    }

    .column-mistake .panel-header {
      border-color: #dc2626;
    }

    .panel-title {
      font-size: 15px;
      font-weight: 700;
      display: flex;
      align-items: center;
      gap: 6px;
    }

    .column-correct .panel-title { color: #15803d; }
    .column-mistake .panel-title { color: #b91c1c; }

    .badge {
      font-size: 11px;
      font-weight: 700;
      padding: 3px 8px;
      border-radius: 999px;
      letter-spacing: 0.3px;
      text-transform: uppercase;
    }

    .badge-correct {
      background: #dcfce7;
      color: #15803d;
    }

    .badge-warning {
      background: #fee2e2;
      color: #b91c1c;
    }

    /* Math Cards */
    .math-card {
      background: #f8fafc;
      border-left: 4px solid #94a3b8;
      border-radius: 6px;
      padding: 10px 12px;
      display: flex;
      flex-direction: column;
      gap: 4px;
      transition: background-color 0.15s ease;
    }

    .math-card.correct-item {
      background: #f0fdf4;
      border-left-color: #16a34a;
    }

    .math-card.mistake-item {
      background: #fef2f2;
      border-left-color: #ef4444;
    }

    .card-main {
      display: flex;
      align-items: center;
      justify-content: space-between;
      gap: 8px;
    }

    .step-label {
      font-size: 11px;
      font-weight: 600;
      color: #64748b;
      text-transform: uppercase;
      letter-spacing: 0.4px;
    }

    .status-icon {
      display: inline-flex;
      align-items: center;
      justify-content: center;
      width: 22px;
      height: 22px;
      border-radius: 50%;
      font-size: 13px;
      font-weight: 800;
      flex-shrink: 0;
    }

    .icon-green {
      background: #dcfce7;
      color: #16a34a;
    }

    .icon-red {
      background: #fee2e2;
      color: #dc2626;
    }

    /* High-contrast Math Typography */
    .math-text {
      font-family: "Cambria Math", "STIX Two Math", "Times New Roman", Georgia, serif;
      font-size: 17px;
      color: #0f172a;
      letter-spacing: 0.2px;
      display: inline-flex;
      align-items: center;
      flex-wrap: wrap;
      gap: 2px;
    }

    .math-var {
      font-style: italic;
      font-family: "Cambria Math", "Times New Roman", serif;
      padding: 0 1px;
    }

    .math-base {
      font-size: 12px;
      position: relative;
      bottom: -4px;
      margin-right: 2px;
      font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      font-weight: 600;
      color: #334155;
    }

    .frac {
      display: inline-flex;
      flex-direction: column;
      vertical-align: middle;
      text-align: center;
      padding: 0 3px;
      font-size: 0.9em;
      line-height: 1;
    }

    .frac .num {
      border-bottom: 1.5px solid #0f172a;
      padding-bottom: 2px;
      display: block;
    }

    .frac .den {
      padding-top: 2px;
      display: block;
    }

    .op {
      margin: 0 4px;
      font-family: system-ui, sans-serif;
      font-weight: 600;
    }

    .neq {
      color: #dc2626;
      font-weight: 700;
      margin: 0 6px;
      font-size: 19px;
    }

    .card-footer {
      font-size: 12px;
      font-weight: 500;
      color: #475569;
      display: flex;
      align-items: center;
      gap: 4px;
      margin-top: 2px;
    }

    .tag-error {
      display: inline-block;
      font-size: 11px;
      font-weight: 700;
      color: #991b1b;
      background: #fee2e2;
      padding: 2px 6px;
      border-radius: 4px;
      width: fit-content;
    }

    .verify-box {
      background: #f0fdf4;
      border: 1.5px dashed #86efac;
      border-radius: 6px;
      padding: 8px 12px;
      display: flex;
      align-items: center;
      justify-content: space-between;
      font-size: 13px;
      color: #166534;
      font-weight: 600;
    }
  </style>
</head>
<body>

  <div class="container">
    
    <div class="column column-correct">
      <div class="panel-header">
        <div class="panel-title">
          <span>Quotient Rule</span>
        </div>
        <span class="badge badge-correct">Correct Rule</span>
      </div>

      
      <div class="math-card correct-item">
        <span class="step-label">Step 1: Given Expression</span>
        <div class="card-main">
          <div class="math-text">
            log<span class="math-base">3</span><span style="font-size: 20px;">(</span><span class="frac"><span class="num">81</span><span class="den">9</span></span><span style="font-size: 20px;">)</span>
          </div>
          <span class="status-icon icon-green">✓</span>
        </div>
      </div>

      
      <div class="math-card correct-item">
        <span class="step-label">Step 2: Expand with Subtraction</span>
        <div class="card-main">
          <div class="math-text">
            <span class="op">=</span> log<span class="math-base">3</span>(81) <span class="op">−</span> log<span class="math-base">3</span>(9)
          </div>
          <span class="status-icon icon-green">✓</span>
        </div>
      </div>

      
      <div class="math-card correct-item">
        <span class="step-label">Step 3: Evaluate Each Term</span>
        <div class="card-main">
          <div class="math-text">
            <span class="op">=</span> 4 <span class="op">−</span> 2 <span class="op">=</span> <strong>2</strong>
          </div>
          <span class="status-icon icon-green">✓</span>
        </div>
      </div>

      
      <div class="verify-box">
        <div class="math-text" style="font-size: 14px; color: #166534;">
          Check: log<span class="math-base">3</span>(9) <span class="op">=</span> 2
        </div>
        <span>✓ Matches Direct Division</span>
      </div>
    </div>

    
    <div class="column column-mistake">
      <div class="panel-header">
        <div class="panel-title">
          <span>Common Mistake Alert</span>
        </div>
        <span class="badge badge-warning">Watch Out</span>
      </div>

      
      <div class="math-card mistake-item">
        <div class="card-main">
          <div class="math-text">
            log<span class="math-base"><span class="math-var">b</span></span><span style="font-size: 19px;">(</span><span class="frac"><span class="num"><span class="math-var">M</span></span><span class="den"><span class="math-var">N</span></span></span><span style="font-size: 19px;">)</span>
            <span class="neq">≠</span>
            <span class="frac"><span class="num">log<span class="math-base"><span class="math-var">b</span></span>(<span class="math-var">M</span>)</span><span class="den">log<span class="math-base"><span class="math-var">b</span></span>(<span class="math-var">N</span>)</span></span>
          </div>
          <span class="status-icon icon-red">✕</span>
        </div>
        <div class="card-footer">
          <span class="tag-error">NOT a quotient of logs</span>
        </div>
      </div>

      
      <div class="math-card mistake-item">
        <div class="card-main">
          <div class="math-text">
            log<span class="math-base"><span class="math-var">b</span></span>(<span class="math-var">M</span> <span class="op">−</span> <span class="math-var">N</span>)
            <span class="neq">≠</span>
            log<span class="math-base"><span class="math-var">b</span></span>(<span class="math-var">M</span>) <span class="op">−</span> log<span class="math-base"><span class="math-var">b</span></span>(<span class="math-var">N</span>)
          </div>
          <span class="status-icon icon-red">✕</span>
        </div>
        <div class="card-footer">
          <span class="tag-error">Logs do NOT distribute</span>
        </div>
      </div>

      
      <div class="math-card" style="background: #fffbeb; border-left-color: #f59e0b;">
        <span class="step-label" style="color: #b45309;">Key Takeaway</span>
        <div style="font-size: 13px; color: #92400e; font-weight: 500;">
          The log of a quotient becomes a <strong>difference of logs</strong>, not a division or distributed minus.
        </div>
      </div>
    </div>
  </div>

</body>
</html>

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <title>Power Rule of Logarithms</title>
  <style>
    * {
      box-sizing: border-box;
      margin: 0;
      padding: 0;
    }

    body {
      font-family: system-ui, -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, sans-serif;
      color: #1e2945;
      background: transparent;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      min-height: 100vh;
      padding: 12px 8px;
      user-select: none;
    }

    .wrapper {
      width: 100%;
      max-width: 480px;
      display: flex;
      flex-direction: column;
      gap: 12px;
    }

    /* Subscript and Superscript typography */
    sub {
      font-size: 0.65em;
      vertical-align: -0.3em;
      line-height: 0;
      color: #64748b;
      font-family: inherit;
    }

    sup {
      font-size: 0.65em;
      vertical-align: 0.45em;
      line-height: 0;
      font-family: inherit;
    }

    /* Main visual stage */
    .stage {
      background: #ffffff;
      border: 1px solid #e2e8f0;
      border-radius: 14px;
      padding: 18px 12px 16px;
      box-shadow: 0 4px 16px rgba(0, 0, 0, 0.04);
      display: flex;
      flex-direction: column;
      align-items: center;
      position: relative;
    }

    .badge {
      font-size: 11px;
      font-weight: 700;
      text-transform: uppercase;
      letter-spacing: 0.06em;
      color: #4f46e5;
      background: #eef2ff;
      padding: 4px 10px;
      border-radius: 999px;
      margin-bottom: 10px;
    }

    /* Formula display area */
    .formula-box {
      position: relative;
      height: 72px;
      width: 100%;
      max-width: 360px;
      display: flex;
      align-items: center;
      justify-content: center;
      font-family: 'Cambria Math', 'KaTeX_Math', 'Times New Roman', Georgia, serif;
      font-size: clamp(26px, 7vw, 32px);
      font-weight: 600;
    }

    /* SVG Arc overlay */
    .arc-svg {
      position: absolute;
      top: -4px;
      left: 50%;
      transform: translateX(-50%);
      width: 250px;
      height: 56px;
      pointer-events: none;
      overflow: visible;
    }

    .arc-path {
      fill: none;
      stroke: #818cf8;
      stroke-width: 2.5;
      stroke-dasharray: 5 4;
      opacity: 0;
      transition: opacity 0.35s ease;
    }

    .arc-path.active {
      opacity: 0.95;
    }

    .arc-arrow {
      fill: #4f46e5;
      opacity: 0;
      transition: opacity 0.35s ease;
    }

    .arc-arrow.active {
      opacity: 1;
    }

    /* Math terms */
    .math-row {
      display: flex;
      align-items: baseline;
      justify-content: center;
      position: relative;
    }

    .log-text {
      color: #1e2945;
      font-style: normal;
    }

    .paren {
      color: #475569;
      font-weight: 400;
    }

    .base-m {
      color: #0f172a;
      font-style: italic;
    }

    /* Moving K element */
    .k-wrap {
      position: absolute;
      transition: transform 0.75s cubic-bezier(0.34, 1.35, 0.64, 1), opacity 0.3s ease;
      color: #4f46e5;
      font-style: italic;
      font-weight: 700;
      display: inline-flex;
      align-items: center;
      justify-content: center;
    }

    .k-wrap .dot-mult {
      opacity: 0;
      font-size: 0.8em;
      margin-left: 3px;
      color: #64748b;
      transition: opacity 0.3s ease;
    }

    /* Positions for algebraic k */
    .k-pos-exp {
      transform: translate(58px, -13px) scale(0.72);
    }

    .k-pos-front {
      transform: translate(-98px, 0px) scale(1);
    }

    .k-pos-front .dot-mult {
      opacity: 1;
    }

    /* Concrete example box */
    .example-card {
      background: #f8fafc;
      border: 1px solid #e2e8f0;
      border-radius: 12px;
      padding: 12px 14px;
      width: 100%;
      display: flex;
      flex-direction: column;
      gap: 8px;
    }

    .example-header {
      display: flex;
      justify-content: space-between;
      align-items: center;
    }

    .example-title {
      font-size: 11px;
      font-weight: 700;
      letter-spacing: 0.05em;
      text-transform: uppercase;
      color: #64748b;
    }

    .example-params {
      font-size: 11px;
      color: #94a3b8;
      font-family: 'Cambria Math', Georgia, serif;
    }

    .example-flow {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: clamp(2px, 1vw, 6px);
      font-family: 'Cambria Math', 'KaTeX_Math', 'Times New Roman', Georgia, serif;
      font-size: clamp(12.5px, 3.5vw, 16px);
      font-weight: 600;
      width: 100%;
      flex-wrap: wrap;
    }

    .ex-step {
      display: inline-flex;
      align-items: center;
      padding: 4px clamp(5px, 1.5vw, 8px);
      background: #ffffff;
      border: 1.5px solid #e2e8f0;
      border-radius: 7px;
      transition: border-color 0.3s ease, background-color 0.3s ease, color 0.3s ease, box-shadow 0.3s ease;
      color: #334155;
      line-height: 1.2;
    }

    .ex-step.active {
      border-color: #4f46e5;
      background: #eef2ff;
      color: #1e1b4b;
      box-shadow: 0 2px 6px rgba(79, 70, 229, 0.15);
    }

    .eq-sign {
      color: #94a3b8;
      font-weight: 400;
      font-size: clamp(12px, 3.4vw, 15px);
      flex-shrink: 0;
      padding: 0 1px;
    }

    .indigo-val {
      color: #4f46e5;
      font-weight: 700;
    }

    /* Interactive Stepper Controls */
    .controls {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 6px;
      width: 100%;
      flex-wrap: wrap;
    }

    .btn {
      background: #ffffff;
      border: 1.5px solid #cbd5e1;
      border-radius: 8px;
      padding: 7px 11px;
      font-size: clamp(11.5px, 3.2vw, 13px);
      font-weight: 600;
      color: #334155;
      cursor: pointer;
      display: inline-flex;
      align-items: center;
      justify-content: center;
      gap: 4px;
      transition: background-color 0.2s ease, border-color 0.2s ease, color 0.2s ease;
    }

    .btn:hover {
      border-color: #94a3b8;
      background: #f8fafc;
    }

    .btn.active {
      background: #4f46e5;
      border-color: #4f46e5;
      color: #ffffff;
    }

    .btn-play {
      padding: 7px 10px;
      font-size: 13px;
    }

    @media (max-width: 360px) {
      .stage {
        padding: 14px 8px 12px;
      }
      .example-card {
        padding: 10px 8px;
      }
      .btn {
        padding: 6px 8px;
      }
    }
  </style>
</head>
<body>

  <div class="wrapper">
    
    <div class="stage">
      <div class="badge">Power Rule Mechanism</div>

      <div class="formula-box">
        
        <svg class="arc-svg" viewBox="0 0 250 56">
          <path id="arcPath" class="arc-path" d="M 182 26 C 150 -8, 75 -8, 34 22" />
          <polygon id="arcArrow" class="arc-arrow" points="30,26 40,18 38,27" />
        </svg>

        
        <div class="math-row">
          
          <div style="width: 28px; height: 1px;"></div>

          <span class="log-text">log</span><sub>b</sub><span class="paren">(</span><span class="base-m">M</span><span class="paren">)</span>

          
          <div style="width: 18px; height: 1px;"></div>

          
          <div id="kElement" class="k-wrap k-pos-exp">
            k<span class="dot-mult">·</span>
          </div>
        </div>
      </div>
    </div>

    
    <div class="example-card">
      <div class="example-header">
        <span class="example-title">Concrete Example</span>
        <span class="example-params">b=5, M=25, k=4</span>
      </div>
      <div class="example-flow">
        <div id="ex1" class="ex-step active">
          log<sub>5</sub>(25<sup class="indigo-val">4</sup>)
        </div>
        <span class="eq-sign">=</span>
        <div id="ex2" class="ex-step">
          <span class="indigo-val">4</span>&thinsp;·&thinsp;log<sub>5</sub>(25)
        </div>
        <span class="eq-sign">=</span>
        <div id="ex3" class="ex-step">
          <span class="indigo-val">4</span>&thinsp;·&thinsp;2
        </div>
        <span class="eq-sign">=</span>
        <div id="ex4" class="ex-step">
          <span class="indigo-val">8</span>
        </div>
      </div>
    </div>

    
    <div class="controls">
      <button id="btnPlay" class="btn btn-play" title="Auto play / pause" aria-label="Play or Pause">⏸</button>
      <button id="btnStep1" class="btn active">1. Exponent</button>
      <button id="btnStep2" class="btn">2. Move to Front</button>
      <button id="btnStep3" class="btn">3. Evaluate</button>
    </div>
  </div>

  <script>
    const kEl = document.getElementById('kElement');
    const arcPath = document.getElementById('arcPath');
    const arcArrow = document.getElementById('arcArrow');

    const ex1 = document.getElementById('ex1');
    const ex2 = document.getElementById('ex2');
    const ex3 = document.getElementById('ex3');
    const ex4 = document.getElementById('ex4');

    const btnPlay = document.getElementById('btnPlay');
    const btnStep1 = document.getElementById('btnStep1');
    const btnStep2 = document.getElementById('btnStep2');
    const btnStep3 = document.getElementById('btnStep3');
    const stepBtns = [btnStep1, btnStep2, btnStep3];

    let currentStep = 0;
    let isPlaying = true;
    let timer = null;

    function setStep(step) {
      currentStep = step;

      stepBtns.forEach((b, i) => {
        if (i === step) {
          b.classList.add('active');
        } else {
          b.classList.remove('active');
        }
      });

      [ex1, ex2, ex3, ex4].forEach(el => el.classList.remove('active'));

      if (step === 0) {
        kEl.classList.remove('k-pos-front');
        kEl.classList.add('k-pos-exp');
        arcPath.classList.remove('active');
        arcArrow.classList.remove('active');
        ex1.classList.add('active');
      } else if (step === 1) {
        arcPath.classList.add('active');
        arcArrow.classList.add('active');
        kEl.classList.remove('k-pos-exp');
        kEl.classList.add('k-pos-front');
        ex2.classList.add('active');
      } else if (step === 2) {
        arcPath.classList.remove('active');
        arcArrow.classList.remove('active');
        kEl.classList.remove('k-pos-exp');
        kEl.classList.add('k-pos-front');
        ex3.classList.add('active');
        ex4.classList.add('active');
      }
    }

    function nextStep() {
      const next = (currentStep + 1) % 3;
      setStep(next);
    }

    function startAutoPlay() {
      stopAutoPlay();
      isPlaying = true;
      btnPlay.textContent = '⏸';
      timer = setInterval(nextStep, 3000);
    }

    function stopAutoPlay() {
      isPlaying = false;
      btnPlay.textContent = '▶';
      if (timer) {
        clearInterval(timer);
        timer = null;
      }
    }

    btnStep1.addEventListener('click', () => {
      stopAutoPlay();
      setStep(0);
    });

    btnStep2.addEventListener('click', () => {
      stopAutoPlay();
      setStep(1);
    });

    btnStep3.addEventListener('click', () => {
      stopAutoPlay();
      setStep(2);
    });

    btnPlay.addEventListener('click', () => {
      if (isPlaying) {
        stopAutoPlay();
      } else {
        nextStep();
        startAutoPlay();
      }
    });

    startAutoPlay();
  </script>
</body>
</html>

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <title>Bidirectional Logarithm Operations</title>
  <style>
    * {
      box-sizing: border-box;
      margin: 0;
      padding: 0;
    }
    body {
      font-family: system-ui, -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, sans-serif;
      background: #f8fafc;
      color: #1e293b;
      padding: 12px;
      display: flex;
      flex-direction: column;
      gap: 10px;
      min-height: 100%;
    }
    .grid {
      display: grid;
      grid-template-columns: repeat(auto-fit, minmax(280px, 1fr));
      gap: 12px;
      width: 100%;
    }
    .card-panel {
      background: #ffffff;
      border-radius: 12px;
      border: 1.5px solid #e2e8f0;
      padding: 12px 14px;
      display: flex;
      flex-direction: column;
      gap: 8px;
      box-shadow: 0 2px 6px rgba(0, 0, 0, 0.04);
    }
    .card-panel.indigo-theme {
      border-top: 4px solid #4f46e5;
    }
    .card-panel.teal-theme {
      border-top: 4px solid #0d9488;
    }
    .header-row {
      display: flex;
      align-items: center;
      justify-content: space-between;
      padding-bottom: 2px;
    }
    .tag {
      font-size: 12px;
      font-weight: 700;
      letter-spacing: 0.5px;
      text-transform: uppercase;
      padding: 3px 10px;
      border-radius: 999px;
    }
    .tag-indigo {
      background: #eef2ff;
      color: #4f46e5;
    }
    .tag-teal {
      background: #ccfbf1;
      color: #0f766e;
    }
    .direction-badge {
      font-size: 11px;
      font-weight: 600;
      color: #64748b;
      display: flex;
      align-items: center;
      gap: 4px;
    }
    .math-flow {
      display: flex;
      flex-direction: column;
      gap: 6px;
    }
    .math-box {
      background: #f8fafc;
      border: 1.5px solid #e2e8f0;
      border-radius: 8px;
      padding: 8px 10px;
      display: flex;
      align-items: center;
      justify-content: center;
      min-height: 46px;
      cursor: pointer;
      user-select: none;
      transition: background-color 0.2s ease, border-color 0.2s ease, box-shadow 0.2s ease;
    }
    .math-box:hover {
      background: #f1f5f9;
    }
    .math-box.active-indigo {
      background: #eef2ff;
      border-color: #6366f1;
      box-shadow: 0 0 0 2px rgba(79, 70, 229, 0.18);
    }
    .math-box.active-teal {
      background: #f0fdfa;
      border-color: #14b8a6;
      box-shadow: 0 0 0 2px rgba(13, 148, 136, 0.18);
    }
    
    /* Math Formula Typography */
    .math-expr {
      font-family: 'Cambria Math', 'Times New Roman', Georgia, serif;
      font-size: 15px;
      color: #0f172a;
      display: inline-flex;
      align-items: center;
      justify-content: center;
      white-space: nowrap;
    }
    .math-expr var {
      font-style: italic;
      font-family: 'Cambria Math', 'Times New Roman', Georgia, serif;
      padding: 0 1px;
    }
    .math-expr sub {
      font-size: 0.72em;
      vertical-align: -0.3em;
      margin-left: 1px;
    }
    .math-expr sup {
      font-size: 0.72em;
      vertical-align: 0.45em;
      margin-left: 1px;
    }
    .math-expr .frac {
      display: inline-flex;
      flex-direction: column;
      vertical-align: middle;
      text-align: center;
      padding: 0 2px;
      line-height: 1;
      font-size: 0.9em;
      margin: 0 2px;
    }
    .math-expr .frac-num {
      border-bottom: 1.2px solid currentColor;
      padding-bottom: 2px;
    }
    .math-expr .frac-den {
      padding-top: 2px;
    }
    .math-expr .big-paren {
      font-size: 1.5em;
      font-weight: 300;
      line-height: 1;
      vertical-align: middle;
      font-family: system-ui, -apple-system, sans-serif;
      color: #334155;
    }
    .math-expr .sqrt-bar {
      border-top: 1.2px solid currentColor;
      padding-top: 1px;
      margin-left: -1px;
      display: inline-block;
    }
    .math-op {
      margin: 0 3px;
      font-family: system-ui, -apple-system, sans-serif;
    }

    .arrow-divider {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 6px;
      color: #94a3b8;
      font-size: 12px;
      font-weight: 700;
      padding: 0;
    }
    .arrow-icon {
      font-size: 14px;
      font-weight: bold;
    }
    .indigo-arrow {
      color: #4f46e5;
    }
    .teal-arrow {
      color: #0d9488;
    }
    .law-pill {
      font-size: 11px;
      font-weight: 600;
      color: #475569;
      background: #f1f5f9;
      padding: 1px 8px;
      border-radius: 6px;
      border: 1px solid #e2e8f0;
    }
    .subtext {
      display: flex;
      justify-content: space-between;
      align-items: center;
      font-size: 11px;
      font-weight: 500;
      color: #64748b;
      margin-top: 2px;
      padding-top: 4px;
      border-top: 1px dashed #e2e8f0;
    }
    .interactive-hint {
      text-align: center;
      font-size: 11px;
      font-weight: 600;
      color: #64748b;
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 4px;
      padding: 2px 0;
    }

    @media (max-width: 420px) {
      body {
        padding: 8px;
        gap: 8px;
      }
      .math-expr {
        font-size: 13.5px;
      }
      .card-panel {
        padding: 10px;
      }
    }
  </style>
</head>
<body>

  <div class="grid">
    
    <div class="card-panel indigo-theme">
      <div class="header-row">
        <span class="tag tag-indigo">Expanding</span>
        <span class="direction-badge">Single log &rarr; Multiple logs</span>
      </div>

      <div class="math-flow">
        
        <div class="math-box active-indigo" id="exp-start" onclick="userSelectStep(0)">
          <div class="math-expr">
            log<sub><var>b</var></sub>
            <span class="big-paren">(</span>
            <span class="frac">
              <span class="frac-num"><var>x</var><sup>2</sup>&radic;<span class="sqrt-bar"><var>y</var></span></span>
              <span class="frac-den"><var>z</var><sup>3</sup></span>
            </span>
            <span class="big-paren">)</span>
          </div>
        </div>

        <div class="arrow-divider">
          <span class="arrow-icon indigo-arrow">&darr;</span>
          <span class="law-pill">Product &amp; Quotient Laws</span>
        </div>

        
        <div class="math-box" id="exp-mid" onclick="userSelectStep(1)">
          <div class="math-expr">
            log<sub><var>b</var></sub>(<var>x</var><sup>2</sup>)
            <span class="math-op">+</span>
            log<sub><var>b</var></sub>(<var>y</var><sup>1/2</sup>)
            <span class="math-op">&minus;</span>
            log<sub><var>b</var></sub>(<var>z</var><sup>3</sup>)
          </div>
        </div>

        <div class="arrow-divider">
          <span class="arrow-icon indigo-arrow">&darr;</span>
          <span class="law-pill">Power Law</span>
        </div>

        
        <div class="math-box" id="exp-end" onclick="userSelectStep(2)">
          <div class="math-expr">
            2 log<sub><var>b</var></sub>(<var>x</var>)
            <span class="math-op">+</span>
            <span class="frac"><span class="frac-num">1</span><span class="frac-den">2</span></span>
            log<sub><var>b</var></sub>(<var>y</var>)
            <span class="math-op">&minus;</span>
            3 log<sub><var>b</var></sub>(<var>z</var>)
          </div>
        </div>
      </div>

      <div class="subtext">
        <span>Multiply &rarr; Add (+)</span>
        <span>Divide &rarr; Subtract (&minus;)</span>
      </div>
    </div>

    
    <div class="card-panel teal-theme">
      <div class="header-row">
        <span class="tag tag-teal">Condensing</span>
        <span class="direction-badge">Multiple logs &rarr; Single log</span>
      </div>

      <div class="math-flow">
        
        <div class="math-box active-teal" id="cond-start" onclick="userSelectStep(0)">
          <div class="math-expr">
            3 log<sub><var>b</var></sub>(<var>u</var>)
            <span class="math-op">&minus;</span>
            2 log<sub><var>b</var></sub>(<var>v</var>)
          </div>
        </div>

        <div class="arrow-divider">
          <span class="arrow-icon teal-arrow">&darr;</span>
          <span class="law-pill">Power Law (Reverse)</span>
        </div>

        
        <div class="math-box" id="cond-mid" onclick="userSelectStep(1)">
          <div class="math-expr">
            log<sub><var>b</var></sub>(<var>u</var><sup>3</sup>)
            <span class="math-op">&minus;</span>
            log<sub><var>b</var></sub>(<var>v</var><sup>2</sup>)
          </div>
        </div>

        <div class="arrow-divider">
          <span class="arrow-icon teal-arrow">&darr;</span>
          <span class="law-pill">Quotient Law (Reverse)</span>
        </div>

        
        <div class="math-box" id="cond-end" onclick="userSelectStep(2)">
          <div class="math-expr">
            log<sub><var>b</var></sub>
            <span class="big-paren">(</span>
            <span class="frac">
              <span class="frac-num"><var>u</var><sup>3</sup></span>
              <span class="frac-den"><var>v</var><sup>2</sup></span>
            </span>
            <span class="big-paren">)</span>
          </div>
        </div>
      </div>

      <div class="subtext">
        <span>Coefficients &rarr; Powers</span>
        <span>Subtract (&minus;) &rarr; Divide</span>
      </div>
    </div>
  </div>

  <div class="interactive-hint">
    <span>✦ Tap any step to inspect corresponding operations ✦</span>
  </div>

  <script>
    const expBoxes = ['exp-start', 'exp-mid', 'exp-end'];
    const condBoxes = ['cond-start', 'cond-mid', 'cond-end'];
    let autoCycleTimer = null;
    let currentStep = 0;

    function applyStep(idx) {
      currentStep = idx;
      expBoxes.forEach((id, i) => {
        const el = document.getElementById(id);
        if (el) {
          if (i === idx) {
            el.classList.add('active-indigo');
          } else {
            el.classList.remove('active-indigo');
          }
        }
      });

      condBoxes.forEach((id, i) => {
        const el = document.getElementById(id);
        if (el) {
          if (i === idx) {
            el.classList.add('active-teal');
          } else {
            el.classList.remove('active-teal');
          }
        }
      });
    }

    function userSelectStep(idx) {
      applyStep(idx);
      // Reset timer on user interaction
      clearInterval(autoCycleTimer);
      startAutoCycle();
    }

    function startAutoCycle() {
      autoCycleTimer = setInterval(() => {
        currentStep = (currentStep + 1) % 3;
        applyStep(currentStep);
      }, 4000);
    }

    startAutoCycle();
  </script>
</body>
</html>

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="4:3">
  <style>
    * {
      box-sizing: border-box;
      margin: 0;
      padding: 0;
      -webkit-tap-highlight-color: transparent;
      user-select: none;
    }

    body {
      font-family: system-ui, -apple-system, sans-serif;
      background: #ffffff;
      color: #1e293b;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      min-height: 100%;
      padding: 16px 12px;
      overflow-x: hidden;
    }

    /* Preset switcher */
    .presets {
      display: flex;
      flex-wrap: wrap;
      gap: 6px;
      justify-content: center;
      margin-bottom: 8px;
    }

    .preset-btn {
      background: #f1f5f9;
      border: 1px solid #cbd5e1;
      border-radius: 20px;
      padding: 5px 12px;
      font-size: 13px;
      font-weight: 600;
      color: #475569;
      cursor: pointer;
      transition: all 0.2s ease;
    }

    .preset-btn.active {
      background: #0f172a;
      color: #ffffff;
      border-color: #0f172a;
    }

    /* Legend / Role Badges */
    .legend {
      display: flex;
      gap: 8px;
      justify-content: center;
      flex-wrap: wrap;
      margin-bottom: 12px;
    }

    .chip {
      display: inline-flex;
      align-items: center;
      gap: 6px;
      padding: 6px 12px;
      border-radius: 8px;
      font-size: 13px;
      font-weight: 700;
      cursor: pointer;
      transition: transform 0.2s ease, box-shadow 0.2s ease, opacity 0.2s ease;
      box-shadow: 0 1px 2px rgba(0,0,0,0.05);
    }

    .chip.base {
      background: #e0f2fe;
      color: #0284c7;
      border: 1.5px solid #0284c7;
    }

    .chip.exp {
      background: #ede9fe;
      color: #7c3aed;
      border: 1.5px solid #7c3aed;
    }

    .chip.res {
      background: #fef3c7;
      color: #d97706;
      border: 1.5px solid #d97706;
    }

    .chip.dimmed {
      opacity: 0.35;
    }

    /* Stage Area */
    .stage {
      position: relative;
      width: 100%;
      max-width: 580px;
      flex-grow: 1;
      display: flex;
      flex-direction: column;
      justify-content: center;
      min-height: 220px;
    }

    .equations-container {
      display: grid;
      grid-template-columns: 1fr auto 1fr;
      align-items: center;
      gap: 8px;
      position: relative;
      z-index: 2;
    }

    .eq-card {
      background: #f8fafc;
      border: 1.5px solid #e2e8f0;
      border-radius: 12px;
      padding: 16px 10px;
      text-align: center;
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 10px;
      transition: border-color 0.2s ease;
    }

    .eq-label {
      font-size: 12px;
      font-weight: 700;
      text-transform: uppercase;
      letter-spacing: 0.05em;
      color: #64748b;
    }

    .math-display {
      font-family: "Cambria Math", "KaTeX_Math", "Times New Roman", serif;
      font-size: 32px;
      line-height: 1;
      display: inline-flex;
      align-items: baseline;
      justify-content: center;
    }

    .symbol {
      display: inline-block;
      padding: 3px 6px;
      border-radius: 6px;
      font-weight: 700;
      cursor: pointer;
      transition: all 0.2s ease;
    }

    .sym-base {
      color: #0284c7;
      background: #e0f2fe;
    }

    .sym-exp {
      color: #7c3aed;
      background: #ede9fe;
      font-size: 0.75em;
      vertical-align: super;
      position: relative;
      top: -0.45em;
      margin-left: 1px;
    }

    .sym-res {
      color: #d97706;
      background: #fef3c7;
    }

    .sym-log-base {
      font-size: 0.6em;
      color: #0284c7;
      background: #e0f2fe;
      vertical-align: sub;
      position: relative;
      bottom: -0.3em;
      margin-right: 2px;
    }

    .op {
      margin: 0 4px;
      color: #334155;
      font-family: system-ui, sans-serif;
      font-weight: 400;
    }

    .log-text {
      font-family: system-ui, -apple-system, sans-serif;
      font-weight: 600;
      font-size: 0.9em;
      color: #1e293b;
      margin-right: 2px;
    }

    /* Active highlights */
    .highlighted {
      box-shadow: 0 0 0 2px #0f172a, 0 4px 10px rgba(0,0,0,0.12);
      transform: translateY(-2px);
    }

    .dimmed-sym {
      opacity: 0.3;
    }

    .equiv-arrow {
      font-size: 28px;
      color: #64748b;
      font-weight: bold;
      text-align: center;
    }

    /* SVG Connectors */
    .connector-layer {
      position: absolute;
      top: 0;
      left: 0;
      width: 100%;
      height: 100%;
      z-index: 1;
      pointer-events: none;
    }

    .conn-path {
      fill: none;
      stroke-width: 2.5;
      stroke-linecap: round;
      opacity: 0.25;
      transition: opacity 0.25s ease, stroke-width 0.25s ease;
    }

    .conn-path.path-active {
      opacity: 1;
      stroke-width: 3.5;
    }

    /* Mobile adjustments */
    @media (max-width: 440px) {
      .math-display {
        font-size: 24px;
      }
      .symbol {
        padding: 2px 4px;
      }
      .eq-label {
        font-size: 11px;
      }
      .chip {
        padding: 4px 8px;
        font-size: 12px;
      }
    }
  </style>
</head>
<body>

  
  <div class="presets">
    <button class="preset-btn active" onclick="setPreset(0)">General Form</button>
    <button class="preset-btn" onclick="setPreset(1)">2³ = 8</button>
    <button class="preset-btn" onclick="setPreset(2)">10² = 100</button>
    <button class="preset-btn" onclick="setPreset(3)">3⁴ = 81</button>
  </div>

  
  <div class="legend">
    <div id="chip-base" class="chip base" onclick="toggleFocus('base')">
      <span>●</span> Base
    </div>
    <div id="chip-exp" class="chip exp" onclick="toggleFocus('exp')">
      <span>●</span> Exponent
    </div>
    <div id="chip-res" class="chip res" onclick="toggleFocus('res')">
      <span>●</span> Result
    </div>
  </div>

  
  <div class="stage" id="stage">
    <svg class="connector-layer" id="svgLayer"></svg>

    <div class="equations-container">
      
      <div class="eq-card">
        <div class="eq-label">Exponential Form</div>
        <div class="math-display">
          <span id="exp-b" class="symbol sym-base" onclick="toggleFocus('base')">b</span>
          <span id="exp-k" class="symbol sym-exp" onclick="toggleFocus('exp')">k</span>
          <span class="op">=</span>
          <span id="exp-m" class="symbol sym-res" onclick="toggleFocus('res')">M</span>
        </div>
      </div>

      
      <div class="equiv-arrow">⇄</div>

      
      <div class="eq-card">
        <div class="eq-label">Logarithmic Form</div>
        <div class="math-display">
          <span class="log-text">log</span>
          <span id="log-b" class="symbol sym-log-base" onclick="toggleFocus('base')">b</span>
          <span class="op">(</span>
          <span id="log-m" class="symbol sym-res" onclick="toggleFocus('res')">M</span>
          <span class="op">)</span>
          <span class="op">=</span>
          <span id="log-k" class="symbol sym-exp" style="position:static; font-size:1em; vertical-align:baseline; top:0;" onclick="toggleFocus('exp')">k</span>
        </div>
      </div>
    </div>
  </div>

  <script>
    const data = [
      { b: 'b', k: 'k', m: 'M' },
      { b: '2', k: '3', m: '8' },
      { b: '10', k: '2', m: '100' },
      { b: '3', k: '4', m: '81' }
    ];

    let activeFocus = null;
    let activePreset = 0;

    function setPreset(idx) {
      activePreset = idx;
      document.querySelectorAll('.preset-btn').forEach((btn, i) => {
        btn.classList.toggle('active', i === idx);
      });

      const d = data[idx];
      document.getElementById('exp-b').textContent = d.b;
      document.getElementById('exp-k').textContent = d.k;
      document.getElementById('exp-m').textContent = d.m;

      document.getElementById('log-b').textContent = d.b;
      document.getElementById('log-m').textContent = d.m;
      document.getElementById('log-k').textContent = d.k;

      updateConnectors();
    }

    function toggleFocus(type) {
      if (activeFocus === type) {
        activeFocus = null;
      } else {
        activeFocus = type;
      }
      applyFocus();
    }

    function applyFocus() {
      const types = ['base', 'exp', 'res'];
      const targets = {
        base: ['#chip-base', '#exp-b', '#log-b', '#path-base'],
        exp: ['#chip-exp', '#exp-k', '#log-k', '#path-exp'],
        res: ['#chip-res', '#exp-m', '#log-m', '#path-res']
      };

      types.forEach(t => {
        const isSelected = (activeFocus === t);
        const isNone = (activeFocus === null);

        document.querySelector(`#chip-${t}`).classList.toggle('dimmed', !isSelected && !isNone);

        const expEl = t === 'base' ? '#exp-b' : (t === 'exp' ? '#exp-k' : '#exp-m');
        const logEl = t === 'base' ? '#log-b' : (t === 'exp' ? '#log-k' : '#log-m');
        const pathEl = `#path-${t}`;

        document.querySelector(expEl).classList.toggle('highlighted', isSelected);
        document.querySelector(expEl).classList.toggle('dimmed-sym', !isSelected && !isNone);

        document.querySelector(logEl).classList.toggle('highlighted', isSelected);
        document.querySelector(logEl).classList.toggle('dimmed-sym', !isSelected && !isNone);

        const path = document.querySelector(pathEl);
        if (path) {
          path.classList.toggle('path-active', isSelected || isNone);
          if (!isSelected && !isNone) {
            path.style.opacity = '0.08';
          } else if (isSelected) {
            path.style.opacity = '1';
          } else {
            path.style.opacity = '0.25';
          }
        }
      });
    }

    function getCenter(el, parentRect) {
      const r = el.getBoundingClientRect();
      return {
        x: r.left + r.width / 2 - parentRect.left,
        y: r.top + r.height / 2 - parentRect.top,
        top: r.top - parentRect.top,
        bottom: r.bottom - parentRect.top
      };
    }

    function updateConnectors() {
      const stage = document.getElementById('stage');
      const svg = document.getElementById('svgLayer');
      const stageRect = stage.getBoundingClientRect();

      const eb = getCenter(document.getElementById('exp-b'), stageRect);
      const ek = getCenter(document.getElementById('exp-k'), stageRect);
      const em = getCenter(document.getElementById('exp-m'), stageRect);

      const lb = getCenter(document.getElementById('log-b'), stageRect);
      const lk = getCenter(document.getElementById('log-k'), stageRect);
      const lm = getCenter(document.getElementById('log-m'), stageRect);

      function createArc(p1, p2, curveOffset, color, id) {
        const startY = curveOffset < 0 ? p1.top : p1.bottom;
        const endY = curveOffset < 0 ? p2.top : p2.bottom;
        const midX = (p1.x + p2.x) / 2;
        const midY = (startY + endY) / 2 + curveOffset;

        return `<path id="${id}" class="conn-path ${activeFocus === null || activeFocus === id.replace('path-','') ? 'path-active' : ''}" 
          d="M ${p1.x} ${startY} Q ${midX} ${midY} ${p2.x} ${endY}" 
          stroke="${color}" />`;
      }

      svg.innerHTML = `
        ${createArc(eb, lb, 45, '#0284c7', 'path-base')}
        ${createArc(ek, lk, -55, '#7c3aed', 'path-exp')}
        ${createArc(em, lm, 65, '#d97706', 'path-res')}
      `;

      applyFocus();
    }

    window.addEventListener('resize', updateConnectors);
    window.addEventListener('load', updateConnectors);
    setTimeout(updateConnectors, 50);
  </script>
</body>
</html>

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="4:3">
  <style>
    * {
      box-sizing: border-box;
      margin: 0;
      padding: 0;
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      user-select: none;
      -webkit-user-select: none;
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    body {
      background-color: #f8fafc;
      color: #1e293b;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      min-height: 100%;
      padding: 12px;
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    .container {
      width: 100%;
      max-width: 500px;
      display: flex;
      flex-direction: column;
      gap: 10px;
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      display: flex;
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      background: #ffffff;
      border: 1.5px solid #cbd5e1;
      color: #475569;
      font-size: 14px;
      font-weight: 600;
      padding: 6px 14px;
      border-radius: 20px;
      cursor: pointer;
      transition: all 0.2s ease;
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    .btn-preset.active {
      background: #0f172a;
      border-color: #0f172a;
      color: #ffffff;
      box-shadow: 0 2px 6px rgba(15, 23, 42, 0.15);
    }

    .svg-canvas {
      width: 100%;
      height: auto;
      display: block;
    }

    /* Pill interactive styles */
    .pill-group {
      cursor: pointer;
      transition: opacity 0.25s ease, filter 0.25s ease;
    }

    .pill-bg {
      transition: fill 0.2s ease, stroke 0.2s ease, stroke-width 0.2s ease;
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    .flow-line {
      fill: none;
      stroke-linecap: round;
      stroke-linejoin: round;
      transition: stroke-dashoffset 0.4s ease, opacity 0.3s ease, stroke-width 0.3s ease;
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    .filter-btn-group {
      display: flex;
      justify-content: center;
      gap: 8px;
      margin-top: 2px;
    }

    .filter-btn {
      font-size: 13px;
      font-weight: 600;
      padding: 4px 10px;
      border-radius: 6px;
      border: 1px solid transparent;
      cursor: pointer;
      transition: all 0.2s ease;
      background: #ffffff;
      color: #64748b;
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    .filter-btn.base-btn { color: #0284c7; border-color: #bae6fd; }
    .filter-btn.base-btn.active { background: #0284c7; color: #fff; border-color: #0284c7; }

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</head>
<body>
  <div class="container">
    
    <div class="controls">
      <button class="btn-preset active" onclick="setPreset(0)">General Form</button>
      <button class="btn-preset" onclick="setPreset(1)">2³ = 8</button>
      <button class="btn-preset" onclick="setPreset(2)">10² = 100</button>
    </div>

    
    <svg class="svg-canvas" viewBox="0 0 500 270" xmlns="http://www.w3.org/2000/svg">
      <defs>
        
        <marker id="arrow-b" markerWidth="8" markerHeight="8" refX="5" refY="4" orient="auto">
          <path d="M1,1 L7,4 L1,7 Z" fill="#0284c7" />
        </marker>
        
        <marker id="arrow-y" markerWidth="8" markerHeight="8" refX="5" refY="4" orient="auto">
          <path d="M1,1 L7,4 L1,7 Z" fill="#d97706" />
        </marker>
        
        <marker id="arrow-x" markerWidth="8" markerHeight="8" refX="5" refY="4" orient="auto">
          <path d="M1,1 L7,4 L1,7 Z" fill="#059669" />
        </marker>
      </defs>

      
      <text x="32" y="52" fill="#64748b" font-size="13" font-weight="700" letter-spacing="0.5">EXPONENTIAL</text>
      <text x="32" y="215" fill="#64748b" font-size="13" font-weight="700" letter-spacing="0.5">LOGARITHMIC</text>

      
      
      <path id="path-b" class="flow-line" d="M 188 64 C 188 135, 230 145, 230 196" stroke="#0284c7" stroke-width="2.5" stroke-dasharray="6,4" marker-end="url(#arrow-b)" />

      
      <path id="path-x" class="flow-line" d="M 334 64 C 334 135, 290 135, 290 196" stroke="#059669" stroke-width="2.5" stroke-dasharray="6,4" marker-end="url(#arrow-x)" />

      
      <path id="path-y" class="flow-line" d="M 235 52 C 285 52, 385 110, 385 196" stroke="#d97706" stroke-width="2.5" stroke-dasharray="6,4" marker-end="url(#arrow-y)" />

      
      
      <g id="top-b-grp" class="pill-group" onclick="selectPart('base')">
        <rect id="top-b-rect" class="pill-bg" x="168" y="28" width="40" height="38" rx="8" fill="#e0f2fe" stroke="#0284c7" stroke-width="2" />
        <text id="top-b-val" x="188" y="53" text-anchor="middle" font-size="20" font-weight="700" fill="#0284c7">b</text>
      </g>

      
      <g id="top-y-grp" class="pill-group" onclick="selectPart('exp')">
        <rect id="top-y-rect" class="pill-bg" x="216" y="18" width="38" height="32" rx="7" fill="#fef3c7" stroke="#d97706" stroke-width="2" />
        <text id="top-y-val" x="235" y="40" text-anchor="middle" font-size="16" font-weight="700" fill="#d97706">y</text>
      </g>

      
      <text x="274" y="53" text-anchor="middle" font-size="22" font-weight="600" fill="#64748b">=</text>

      
      <g id="top-x-grp" class="pill-group" onclick="selectPart('res')">
        <rect id="top-x-rect" class="pill-bg" x="306" y="28" width="56" height="38" rx="8" fill="#d1fae5" stroke="#059669" stroke-width="2" />
        <text id="top-x-val" x="334" y="53" text-anchor="middle" font-size="20" font-weight="700" fill="#059669">x</text>
      </g>

      
      
      <text x="188" y="222" text-anchor="middle" font-size="24" font-weight="700" fill="#1e293b">log</text>

      
      <g id="bot-b-grp" class="pill-group" onclick="selectPart('base')">
        <rect id="bot-b-rect" class="pill-bg" x="213" y="206" width="34" height="28" rx="6" fill="#e0f2fe" stroke="#0284c7" stroke-width="2" />
        <text id="bot-b-val" x="230" y="226" text-anchor="middle" font-size="15" font-weight="700" fill="#0284c7">b</text>
      </g>

      
      <text x="257" y="223" text-anchor="middle" font-size="24" font-weight="500" fill="#64748b">(</text>

      
      <g id="bot-x-grp" class="pill-group" onclick="selectPart('res')">
        <rect id="bot-x-rect" class="pill-bg" x="264" y="197" width="52" height="36" rx="8" fill="#d1fae5" stroke="#059669" stroke-width="2" />
        <text id="bot-x-val" x="290" y="222" text-anchor="middle" font-size="19" font-weight="700" fill="#059669">x</text>
      </g>

      
      <text x="325" y="223" text-anchor="middle" font-size="24" font-weight="500" fill="#64748b">)</text>

      
      <text x="345" y="222" text-anchor="middle" font-size="22" font-weight="600" fill="#64748b">=</text>

      
      <g id="bot-y-grp" class="pill-group" onclick="selectPart('exp')">
        <rect id="bot-y-rect" class="pill-bg" x="364" y="197" width="42" height="36" rx="8" fill="#fef3c7" stroke="#d97706" stroke-width="2" />
        <text id="bot-y-val" x="385" y="222" text-anchor="middle" font-size="19" font-weight="700" fill="#d97706">y</text>
      </g>
    </svg>

    
    <div class="filter-btn-group">
      <button class="filter-btn all-btn active" onclick="selectPart('all')">Show All</button>
      <button class="filter-btn base-btn" onclick="selectPart('base')">Base</button>
      <button class="filter-btn exp-btn" onclick="selectPart('exp')">Exponent</button>
      <button class="filter-btn res-btn" onclick="selectPart('res')">Argument</button>
    </div>
  </div>

  <script>
    const presets = [
      { b: 'b', y: 'y', x: 'x' },
      { b: '2', y: '3', x: '8' },
      { b: '10', y: '2', x: '100' }
    ];

    let currentPreset = 0;
    let activePart = 'all';

    function setPreset(idx) {
      currentPreset = idx;
      const p = presets[idx];

      document.getElementById('top-b-val').textContent = p.b;
      document.getElementById('bot-b-val').textContent = p.b;

      document.getElementById('top-y-val').textContent = p.y;
      document.getElementById('bot-y-val').textContent = p.y;

      document.getElementById('top-x-val').textContent = p.x;
      document.getElementById('bot-x-val').textContent = p.x;

      const buttons = document.querySelectorAll('.btn-preset');
      buttons.forEach((btn, i) => {
        btn.classList.toggle('active', i === idx);
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    function selectPart(part) {
      activePart = part;

      // Update button active state
      document.querySelector('.all-btn').classList.toggle('active', part === 'all');
      document.querySelector('.base-btn').classList.toggle('active', part === 'base');
      document.querySelector('.exp-btn').classList.toggle('active', part === 'exp');
      document.querySelector('.res-btn').classList.toggle('active', part === 'res');

      // Highlight logic
      const showBase = part === 'all' || part === 'base';
      const showExp = part === 'all' || part === 'exp';
      const showRes = part === 'all' || part === 'res';

      // Paths
      document.getElementById('path-b').style.opacity = showBase ? '1' : '0.12';
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      document.getElementById('path-b').style.strokeWidth = part === 'base' ? '3.5' : '2.5';
      document.getElementById('path-y').style.strokeWidth = part === 'exp' ? '3.5' : '2.5';
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      // Pills opacity & focus
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      setGroupFocus('top-y-grp', 'bot-y-grp', showExp, part === 'exp');
      setGroupFocus('top-x-grp', 'bot-x-grp', showRes, part === 'res');
    }

    function setGroupFocus(id1, id2, visible, focused) {
      const g1 = document.getElementById(id1);
      const g2 = document.getElementById(id2);
      const opacity = visible ? '1' : '0.25';
      const filter = focused ? 'drop-shadow(0 2px 5px rgba(0,0,0,0.18))' : 'none';

      g1.style.opacity = opacity;
      g2.style.opacity = opacity;
      g1.style.filter = filter;
      g2.style.filter = filter;
    }
  </script>
</body>
</html>

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="1:1">
  <title>Proof of Product Rule for Logarithms</title>
  <style>
    * {
      box-sizing: border-box;
      margin: 0;
      padding: 0;
      font-family: system-ui, -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, sans-serif;
    }
    body {
      background: #f8fafc;
      color: #1e293b;
      padding: 12px;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      min-height: 100%;
      user-select: none;
    }

    /* Container */
    .flow-container {
      width: 100%;
      max-width: 480px;
      display: flex;
      flex-direction: column;
      gap: 8px;
    }

    /* Cards */
    .step-card {
      background: #ffffff;
      border: 2px solid #e2e8f0;
      border-radius: 10px;
      padding: 10px 14px;
      display: flex;
      align-items: center;
      justify-content: space-between;
      gap: 8px;
      transition: all 0.3s ease;
      cursor: pointer;
      opacity: 0.45;
    }
    .step-card.active {
      opacity: 1;
      border-color: #2563eb;
      box-shadow: 0 4px 12px rgba(37, 99, 235, 0.12);
      transform: translateY(-1px);
    }
    .step-card.completed {
      opacity: 0.9;
      border-color: #cbd5e1;
    }

    /* Step Badge */
    .step-num {
      width: 24px;
      height: 24px;
      border-radius: 50%;
      background: #f1f5f9;
      color: #64748b;
      font-weight: 700;
      font-size: 12px;
      display: flex;
      align-items: center;
      justify-content: center;
      flex-shrink: 0;
      transition: all 0.3s ease;
    }
    .step-card.active .step-num {
      background: #2563eb;
      color: #ffffff;
    }
    .step-card.completed .step-num {
      background: #e2e8f0;
      color: #334155;
    }

    /* Math Content */
    .math-content {
      flex: 1;
      font-family: 'Cambria Math', 'KaTeX_Math', 'Times New Roman', Georgia, serif;
      font-size: 17px;
      text-align: center;
      color: #0f172a;
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 6px;
      flex-wrap: wrap;
    }
    .u-var { color: #d97706; font-weight: 600; }
    .v-var { color: #059669; font-weight: 600; }
    .b-var { color: #475569; }
    .add-op {
      color: #2563eb;
      font-weight: 700;
      padding: 0 2px;
      border-radius: 4px;
      background: rgba(37, 99, 235, 0.1);
    }
    .final-box {
      background: #eff6ff;
      border: 1.5px dashed #3b82f6;
      border-radius: 6px;
      padding: 3px 8px;
    }

    /* Connectors */
    .connector {
      text-align: center;
      color: #94a3b8;
      font-size: 14px;
      line-height: 10px;
      height: 10px;
      transition: color 0.3s ease;
    }
    .connector.active {
      color: #2563eb;
      font-weight: bold;
    }

    /* Bottom Toolbar */
    .toolbar {
      width: 100%;
      max-width: 480px;
      margin-top: 10px;
      display: flex;
      align-items: center;
      justify-content: space-between;
      gap: 12px;
      padding: 4px 6px;
    }
    .btn-group {
      display: flex;
      gap: 6px;
    }
    .ctrl-btn {
      background: #ffffff;
      border: 1px solid #cbd5e1;
      border-radius: 6px;
      color: #334155;
      font-size: 13px;
      font-weight: 600;
      padding: 6px 12px;
      cursor: pointer;
      display: flex;
      align-items: center;
      justify-content: center;
      transition: background 0.2s, border-color 0.2s;
    }
    .ctrl-btn:hover {
      background: #f1f5f9;
      border-color: #94a3b8;
    }

    /* Dots */
    .dots-group {
      display: flex;
      gap: 6px;
    }
    .dot {
      width: 10px;
      height: 10px;
      border-radius: 50%;
      background: #cbd5e1;
      cursor: pointer;
      transition: all 0.3s ease;
    }
    .dot.active {
      background: #2563eb;
      transform: scale(1.25);
    }

    @media (max-width: 380px) {
      .math-content { font-size: 15px; }
      .step-card { padding: 8px 10px; }
    }
  </style>
</head>
<body>

  <div class="flow-container">
    
    <div class="step-card active" id="card-0" onclick="goToStep(0)">
      <div class="step-num">1</div>
      <div class="math-content">
        <span><span class="u-var">u</span> = log<sub><span class="b-var">b</span></sub>(x) &hArr; <span class="b-var">b</span><sup><span class="u-var">u</span></sup> = x</span>
        <span style="color:#cbd5e1; margin:0 4px;">|</span>
        <span><span class="v-var">v</span> = log<sub><span class="b-var">b</span></sub>(y) &hArr; <span class="b-var">b</span><sup><span class="v-var">v</span></sup> = y</span>
      </div>
    </div>

    <div class="connector active" id="conn-0">&darr;</div>

    
    <div class="step-card" id="card-1" onclick="goToStep(1)">
      <div class="step-num">2</div>
      <div class="math-content">
        <span>xy = <span class="b-var">b</span><sup><span class="u-var">u</span></sup> &middot; <span class="b-var">b</span><sup><span class="v-var">v</span></sup> = <span class="b-var">b</span><sup><span class="u-var">u</span><span class="add-op">+</span><span class="v-var">v</span></sup></span>
      </div>
    </div>

    <div class="connector" id="conn-1">&darr;</div>

    
    <div class="step-card" id="card-2" onclick="goToStep(2)">
      <div class="step-num">3</div>
      <div class="math-content">
        <span>log<sub><span class="b-var">b</span></sub>(xy) = <span class="u-var">u</span> <span class="add-op">+</span> <span class="v-var">v</span></span>
      </div>
    </div>

    <div class="connector" id="conn-2">&darr;</div>

    
    <div class="step-card" id="card-3" onclick="goToStep(3)">
      <div class="step-num">4</div>
      <div class="math-content final-box">
        <span>log<sub><span class="b-var">b</span></sub>(xy) = log<sub><span class="b-var">b</span></sub>(x) + log<sub><span class="b-var">b</span></sub>(y)</span>
      </div>
    </div>
  </div>

  
  <div class="toolbar">
    <div class="btn-group">
      <button class="ctrl-btn" onclick="prevStep()" aria-label="Previous Step">&#9664;</button>
      <button class="ctrl-btn" id="playBtn" onclick="togglePlay()">&#10074;&#10074;</button>
      <button class="ctrl-btn" onclick="nextStep()" aria-label="Next Step">&#9654;</button>
    </div>

    <div class="dots-group">
      <div class="dot active" onclick="goToStep(0)" title="Step 1"></div>
      <div class="dot" onclick="goToStep(1)" title="Step 2"></div>
      <div class="dot" onclick="goToStep(2)" title="Step 3"></div>
      <div class="dot" onclick="goToStep(3)" title="Step 4"></div>
    </div>
  </div>

  <script>
    let currentStep = 0;
    const totalSteps = 4;
    let isPlaying = true;
    let timer = null;
    const stepDuration = 3500;

    function updateUI() {
      for (let i = 0; i < totalSteps; i++) {
        const card = document.getElementById(`card-${i}`);
        const dot = document.querySelectorAll('.dot')[i];
        
        card.classList.remove('active', 'completed');
        dot.classList.remove('active');

        if (i === currentStep) {
          card.classList.add('active');
          dot.classList.add('active');
        } else if (i < currentStep) {
          card.classList.add('completed');
        }

        if (i < totalSteps - 1) {
          const conn = document.getElementById(`conn-${i}`);
          if (conn) {
            conn.classList.toggle('active', i < currentStep);
          }
        }
      }
    }

    function goToStep(stepIndex) {
      currentStep = stepIndex;
      updateUI();
      if (isPlaying) {
        resetTimer();
      }
    }

    function nextStep() {
      currentStep = (currentStep + 1) % totalSteps;
      updateUI();
      if (isPlaying) resetTimer();
    }

    function prevStep() {
      currentStep = (currentStep - 1 + totalSteps) % totalSteps;
      updateUI();
      if (isPlaying) resetTimer();
    }

    function togglePlay() {
      isPlaying = !isPlaying;
      const playBtn = document.getElementById('playBtn');
      if (isPlaying) {
        playBtn.innerHTML = '&#10074;&#10074;';
        startTimer();
      } else {
        playBtn.innerHTML = '&#9654;';
        clearInterval(timer);
      }
    }

    function startTimer() {
      clearInterval(timer);
      timer = setInterval(() => {
        currentStep = (currentStep + 1) % totalSteps;
        updateUI();
      }, stepDuration);
    }

    function resetTimer() {
      clearInterval(timer);
      timer = setInterval(() => {
        currentStep = (currentStep + 1) % totalSteps;
        updateUI();
      }, stepDuration);
    }

    // Initialize auto-play
    startTimer();
  </script>
</body>
</html>

OGM.12.EXP.3

Aligned learning resources

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