<!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>Inverse Functions: 2^x and log2(x)</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: #1e2945;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      padding: 12px;
      user-select: none;
    }
    .graph-container {
      width: 100%;
      max-width: 440px;
      aspect-ratio: 1 / 1;
      position: relative;
    }
    svg {
      width: 100%;
      height: 100%;
      overflow: visible;
    }
    .grid-line {
      stroke: #e2e8f0;
      stroke-width: 1;
    }
    .axis {
      stroke: #64748b;
      stroke-width: 1.5;
    }
    .tick-label {
      font-size: 11px;
      fill: #94a3b8;
      font-family: inherit;
    }
    .line-diag {
      stroke: #94a3b8;
      stroke-dasharray: 4 4;
      stroke-width: 1.5;
    }
    .curve-exp {
      stroke: #2563eb;
      stroke-width: 2.75;
      fill: none;
      stroke-linecap: round;
    }
    .curve-log {
      stroke: #0d9488;
      stroke-width: 2.75;
      fill: none;
      stroke-linecap: round;
    }
    .connector {
      stroke: #f59e0b;
      stroke-width: 1.5;
      stroke-dasharray: 3 3;
      transition: opacity 0.3s ease;
    }
    .pt-exp {
      fill: #2563eb;
      stroke: #ffffff;
      stroke-width: 2;
      cursor: pointer;
      transition: r 0.2s ease;
    }
    .pt-log {
      fill: #0d9488;
      stroke: #ffffff;
      stroke-width: 2;
      cursor: pointer;
      transition: r 0.2s ease;
    }
    .pt-label {
      font-size: 11px;
      font-weight: 600;
      transition: opacity 0.3s ease;
    }
    .exp-label { fill: #1d4ed8; }
    .log-label { fill: #0f766e; }
    .fn-label {
      font-size: 13px;
      font-weight: 700;
    }
    .btn-row {
      display: flex;
      flex-wrap: wrap;
      gap: 6px;
      justify-content: center;
      margin-top: 10px;
      max-width: 440px;
    }
    .btn {
      appearance: none;
      border: 1px solid #cbd5e1;
      background: #ffffff;
      color: #475569;
      font-size: 12px;
      font-weight: 600;
      padding: 5px 10px;
      border-radius: 6px;
      cursor: pointer;
      transition: background 0.2s, border-color 0.2s, color 0.2s, box-shadow 0.2s;
    }
    .btn:hover {
      background: #f1f5f9;
      border-color: #94a3b8;
    }
    .btn.active {
      background: #0f172a;
      color: #ffffff;
      border-color: #0f172a;
      box-shadow: 0 1px 3px rgba(0,0,0,0.1);
    }
  </style>
</head>
<body>

  <div class="graph-container">
    <svg id="plot" viewBox="0 0 440 440"></svg>
  </div>

  <div class="btn-row" id="controls">
    <button class="btn active" data-pair="all">All</button>
    <button class="btn" data-pair="0">(0, 1) ⇄ (1, 0)</button>
    <button class="btn" data-pair="1">(1, 2) ⇄ (2, 1)</button>
    <button class="btn" data-pair="2">(2, 4) ⇄ (4, 2)</button>
    <button class="btn" data-pair="3">(3, 8) ⇄ (8, 3)</button>
  </div>

  <script>
    const svg = document.getElementById('plot');
    const width = 440;
    const height = 440;
    const pad = 34;

    const xMin = -1.5, xMax = 9.5;
    const yMin = -1.5, yMax = 9.5;

    function toSvgX(x) {
      return pad + ((x - xMin) / (xMax - xMin)) * (width - 2 * pad);
    }
    function toSvgY(y) {
      return height - pad - ((y - yMin) / (yMax - yMin)) * (height - 2 * pad);
    }

    const pairs = [
      { exp: [0, 1], log: [1, 0], expOff: [10, -8], logOff: [10, 14] },
      { exp: [1, 2], log: [2, 1], expOff: [-46, -6], logOff: [8, 14] },
      { exp: [2, 4], log: [4, 2], expOff: [-46, -6], logOff: [8, 14] },
      { exp: [3, 8], log: [8, 3], expOff: [-46, 0], logOff: [8, 14] }
    ];

    let svgContent = '';

    // Grid lines
    for (let i = 0; i <= 9; i++) {
      const gx = toSvgX(i);
      const gy = toSvgY(i);
      svgContent += `<line class="grid-line" x1="${gx}" y1="${toSvgY(yMin)}" x2="${gx}" y2="${toSvgY(yMax)}" />`;
      svgContent += `<line class="grid-line" x1="${toSvgX(xMin)}" y1="${gy}" x2="${toSvgX(xMax)}" y2="${gy}" />`;
    }

    // Axes
    const origX = toSvgX(0);
    const origY = toSvgY(0);
    svgContent += `<line class="axis" x1="${toSvgX(xMin)}" y1="${origY}" x2="${toSvgX(xMax)}" y2="${origY}" />`;
    svgContent += `<line class="axis" x1="${origX}" y1="${toSvgY(yMin)}" x2="${origX}" y2="${toSvgY(yMax)}" />`;

    // Tick labels
    for (let i = 1; i <= 9; i += 2) {
      svgContent += `<text class="tick-label" x="${toSvgX(i)}" y="${origY + 14}" text-anchor="middle">${i}</text>`;
      svgContent += `<text class="tick-label" x="${origX - 8}" y="${toSvgY(i) + 4}" text-anchor="end">${i}</text>`;
    }

    // y = x diagonal
    svgContent += `<line class="line-diag" x1="${toSvgX(-1)}" y1="${toSvgY(-1)}" x2="${toSvgX(9.2)}" y2="${toSvgY(9.2)}" />`;
    svgContent += `<text class="fn-label" fill="#94a3b8" x="${toSvgX(7.8)}" y="${toSvgY(8.6)}" text-anchor="start">y = x</text>`;

    // Sample curves
    let dExp = '';
    for (let x = -1.5; x <= 3.24; x += 0.05) {
      const y = Math.pow(2, x);
      if (y > yMax) break;
      dExp += (dExp === '' ? 'M' : 'L') + ` ${toSvgX(x).toFixed(2)} ${toSvgY(y).toFixed(2)} `;
    }
    svgContent += `<path class="curve-exp" d="${dExp}" />`;

    let dLog = '';
    for (let x = 0.35; x <= xMax; x += 0.05) {
      const y = Math.log2(x);
      dLog += (dLog === '' ? 'M' : 'L') + ` ${toSvgX(x).toFixed(2)} ${toSvgY(y).toFixed(2)} `;
    }
    svgContent += `<path class="curve-log" d="${dLog}" />`;

    // Function labels
    svgContent += `<text class="fn-label exp-label" x="${toSvgX(1.8)}" y="${toSvgY(7.2)}" text-anchor="end">y = 2ˣ</text>`;
    svgContent += `<text class="fn-label log-label" x="${toSvgX(7.2)}" y="${toSvgY(1.8)}" text-anchor="start">y = log₂x</text>`;

    // Connectors & Points
    pairs.forEach((p, idx) => {
      const x1 = toSvgX(p.exp[0]), y1 = toSvgY(p.exp[1]);
      const x2 = toSvgX(p.log[0]), y2 = toSvgY(p.log[1]);

      svgContent += `
        <g id="pair-group-${idx}" class="pair-group">
          <line class="connector" id="conn-${idx}" x1="${x1}" y1="${y1}" x2="${x2}" y2="${y2}" />
          
          <circle class="pt-exp" id="pt-exp-${idx}" cx="${x1}" cy="${y1}" r="4.5" />
          <text class="pt-label exp-label" id="lbl-exp-${idx}" x="${x1 + p.expOff[0]}" y="${y1 + p.expOff[1]}">(${p.exp[0]}, ${p.exp[1]})</text>

          <circle class="pt-log" id="pt-log-${idx}" cx="${x2}" cy="${y2}" r="4.5" />
          <text class="pt-label log-label" id="lbl-log-${idx}" x="${x2 + p.logOff[0]}" y="${y2 + p.logOff[1]}">(${p.log[0]}, ${p.log[1]})</text>
        </g>
      `;
    });

    svg.innerHTML = svgContent;

    // Interactive toggles
    const buttons = document.querySelectorAll('.btn');
    function selectPair(target) {
      buttons.forEach(b => {
        b.classList.toggle('active', b.dataset.pair === String(target));
      });

      pairs.forEach((_, idx) => {
        const show = (target === 'all' || target === String(idx));
        const opacity = show ? '1' : '0.15';
        const connOpacity = show ? '1' : '0';
        const r = (target === String(idx)) ? '6.5' : '4.5';

        document.getElementById(`conn-${idx}`).style.opacity = connOpacity;
        document.getElementById(`pt-exp-${idx}`).style.opacity = opacity;
        document.getElementById(`pt-exp-${idx}`).setAttribute('r', r);
        document.getElementById(`lbl-exp-${idx}`).style.opacity = opacity;
        document.getElementById(`pt-log-${idx}`).style.opacity = opacity;
        document.getElementById(`pt-log-${idx}`).setAttribute('r', r);
        document.getElementById(`lbl-log-${idx}`).style.opacity = opacity;
      });
    }

    buttons.forEach(btn => {
      btn.addEventListener('click', () => selectPair(btn.dataset.pair));
    });

    pairs.forEach((_, idx) => {
      const g = document.getElementById(`pair-group-${idx}`);
      g.style.cursor = 'pointer';
      g.addEventListener('click', () => selectPair(String(idx)));
    });
  </script>
</body>
</html>

Logarithms as Inverses of Exponential Functions

<!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;
    }

    body {
      background-color: #f8fafc;
      color: #1e2945;
      min-height: 100%;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      padding: 12px;
    }

    .grid {
      display: grid;
      grid-template-columns: 1fr;
      gap: 10px;
      width: 100%;
      max-width: 540px;
    }

    .pair-card {
      background: #ffffff;
      border: 1.5px solid #e2e8f0;
      border-radius: 12px;
      padding: 10px 14px;
      display: flex;
      align-items: center;
      justify-content: space-between;
      cursor: pointer;
      user-select: none;
      transition: border-color 0.25s ease, box-shadow 0.25s ease, background-color 0.25s ease;
      box-shadow: 0 1px 3px rgba(0, 0, 0, 0.04);
    }

    .pair-card:hover {
      border-color: #93c5fd;
    }

    .pair-card.active {
      border-color: #0284c7;
      background: #f0f9ff;
      box-shadow: 0 0 0 1px #0284c7, 0 4px 12px rgba(2, 132, 199, 0.12);
    }

    .pair-card.target {
      border-color: #0284c7;
      background: #ffffff;
    }

    .pair-card.target.active {
      background: #e0f2fe;
      border-color: #0284c7;
    }

    .op-side {
      display: flex;
      align-items: center;
      gap: 10px;
      flex: 1;
    }

    .op-side.right {
      justify-content: flex-end;
    }

    .symbol-badge {
      width: 38px;
      height: 38px;
      border-radius: 8px;
      background: #f1f5f9;
      color: #1e2945;
      font-weight: 700;
      font-size: 17px;
      display: flex;
      align-items: center;
      justify-content: center;
      transition: background-color 0.25s ease, color 0.25s ease;
      flex-shrink: 0;
    }

    .pair-card.active .symbol-badge {
      background: #0284c7;
      color: #ffffff;
    }

    .pair-card.target .symbol-badge {
      background: #e0f2fe;
      color: #0284c7;
    }

    .pair-card.target.active .symbol-badge {
      background: #0284c7;
      color: #ffffff;
    }

    .op-label {
      font-size: 14px;
      font-weight: 600;
      color: #334155;
    }

    .pair-card.active .op-label {
      color: #0369a1;
    }

    .undo-bridge {
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      padding: 0 8px;
      position: relative;
      flex-shrink: 0;
      width: 90px;
    }

    .arrow-track {
      position: relative;
      width: 100%;
      height: 18px;
      display: flex;
      align-items: center;
      justify-content: center;
    }

    .arrow-line {
      position: absolute;
      width: 100%;
      height: 2px;
      background: #cbd5e1;
      border-radius: 1px;
    }

    .pair-card.active .arrow-line {
      background: #38bdf8;
    }

    .pulse-dot {
      position: absolute;
      width: 8px;
      height: 8px;
      border-radius: 50%;
      background: #0284c7;
      opacity: 0;
      box-shadow: 0 0 6px #0284c7;
    }

    .pair-card.active .pulse-dot {
      opacity: 1;
      animation: undoOscillate 2.4s ease-in-out infinite;
    }

    .arrow-heads {
      position: absolute;
      width: 100%;
      display: flex;
      justify-content: space-between;
      color: #94a3b8;
      font-size: 13px;
      line-height: 1;
      pointer-events: none;
    }

    .pair-card.active .arrow-heads {
      color: #0284c7;
    }

    .bridge-tag {
      font-size: 11px;
      font-weight: 700;
      text-transform: uppercase;
      letter-spacing: 0.5px;
      color: #64748b;
      margin-top: 1px;
    }

    .pair-card.active .bridge-tag {
      color: #0284c7;
    }

    @keyframes undoOscillate {
      0% { left: 4px; }
      45% { left: calc(100% - 12px); }
      55% { left: calc(100% - 12px); }
      100% { left: 4px; }
    }

    @media (max-width: 420px) {
      .op-label {
        font-size: 12px;
      }
      .symbol-badge {
        width: 32px;
        height: 32px;
        font-size: 14px;
      }
      .undo-bridge {
        width: 70px;
        padding: 0 4px;
      }
      .bridge-tag {
        font-size: 9px;
      }
    }
  </style>
</head>
<body>

  <div class="grid" id="cardGrid">
    
    <div class="pair-card" data-index="0">
      <div class="op-side">
        <div class="symbol-badge">+</div>
        <span class="op-label">Addition</span>
      </div>
      <div class="undo-bridge">
        <div class="arrow-track">
          <div class="arrow-line"></div>
          <div class="pulse-dot"></div>
          <div class="arrow-heads"><span>◀</span><span>▶</span></div>
        </div>
        <span class="bridge-tag">Undoes</span>
      </div>
      <div class="op-side right">
        <span class="op-label">Subtraction</span>
        <div class="symbol-badge">−</div>
      </div>
    </div>

    
    <div class="pair-card" data-index="1">
      <div class="op-side">
        <div class="symbol-badge">×</div>
        <span class="op-label">Multiplication</span>
      </div>
      <div class="undo-bridge">
        <div class="arrow-track">
          <div class="arrow-line"></div>
          <div class="pulse-dot"></div>
          <div class="arrow-heads"><span>◀</span><span>▶</span></div>
        </div>
        <span class="bridge-tag">Undoes</span>
      </div>
      <div class="op-side right">
        <span class="op-label">Division</span>
        <div class="symbol-badge">÷</div>
      </div>
    </div>

    
    <div class="pair-card" data-index="2">
      <div class="op-side">
        <div class="symbol-badge">x²</div>
        <span class="op-label">Squaring</span>
      </div>
      <div class="undo-bridge">
        <div class="arrow-track">
          <div class="arrow-line"></div>
          <div class="pulse-dot"></div>
          <div class="arrow-heads"><span>◀</span><span>▶</span></div>
        </div>
        <span class="bridge-tag">Undoes</span>
      </div>
      <div class="op-side right">
        <span class="op-label">Square Root</span>
        <div class="symbol-badge">√x</div>
      </div>
    </div>

    
    <div class="pair-card target active" data-index="3">
      <div class="op-side">
        <div class="symbol-badge">b<sup>x</sup></div>
        <span class="op-label">Exponential</span>
      </div>
      <div class="undo-bridge">
        <div class="arrow-track">
          <div class="arrow-line"></div>
          <div class="pulse-dot"></div>
          <div class="arrow-heads"><span>◀</span><span>▶</span></div>
        </div>
        <span class="bridge-tag">Undoes</span>
      </div>
      <div class="op-side right">
        <span class="op-label">Logarithm</span>
        <div class="symbol-badge">log<sub>b</sub></div>
      </div>
    </div>
  </div>

  <script>
    const cards = document.querySelectorAll('.pair-card');
    let currentIndex = 3;
    let autoTimer = null;

    function selectCard(index) {
      cards.forEach((card, i) => {
        card.classList.toggle('active', i === index);
      });
      currentIndex = index;
    }

    cards.forEach((card, index) => {
      card.addEventListener('click', () => {
        clearInterval(autoTimer);
        selectCard(index);
        startAutoCycle();
      });
    });

    function startAutoCycle() {
      autoTimer = setInterval(() => {
        currentIndex = (currentIndex + 1) % cards.length;
        selectCard(currentIndex);
      }, 3500);
    }

    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">
  <title>Exponential to Logarithmic Conversion</title>
  <style>
    * {
      box-sizing: border-box;
      margin: 0;
      padding: 0;
      -webkit-tap-highlight-color: transparent;
    }

    body {
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      background: transparent;
      color: #0f172a;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: flex-start;
      min-height: 100%;
      padding: 12px 8px;
      user-select: none;
    }

    /* Container */
    .converter-wrap {
      width: 100%;
      max-width: 400px;
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 10px;
    }

    /* Switcher Controls */
    .controls {
      display: flex;
      gap: 4px;
      background: #f1f5f9;
      padding: 3px;
      border-radius: 8px;
      width: 100%;
      max-width: 340px;
      justify-content: center;
    }

    .tab-btn {
      flex: 1;
      border: none;
      background: transparent;
      padding: 6px 4px;
      border-radius: 6px;
      font-size: 12px;
      font-weight: 600;
      color: #64748b;
      cursor: pointer;
      transition: background 0.15s ease, color 0.15s ease, box-shadow 0.15s ease;
      text-align: center;
      white-space: nowrap;
    }

    .tab-btn.active {
      background: #ffffff;
      color: #0f172a;
      box-shadow: 0 1px 3px rgba(0, 0, 0, 0.1);
    }

    /* Interactive Instruction / Helper */
    .hint-bar {
      font-size: 11.5px;
      font-weight: 500;
      color: #64748b;
      min-height: 16px;
      text-align: center;
      transition: color 0.2s ease;
    }

    .hint-bar.highlight-b { color: #2563eb; font-weight: 600; }
    .hint-bar.highlight-y { color: #ea580c; font-weight: 600; }
    .hint-bar.highlight-x { color: #0d9488; font-weight: 600; }

    /* Main Stage */
    .stage {
      position: relative;
      width: 100%;
      display: flex;
      flex-direction: column;
      gap: 36px;
      align-items: center;
      padding: 4px 0;
    }

    .svg-overlay {
      position: absolute;
      top: 0;
      left: 0;
      width: 100%;
      height: 100%;
      pointer-events: none;
      z-index: 1;
      overflow: visible;
    }

    /* Equation Section */
    .form-card {
      position: relative;
      z-index: 2;
      width: 100%;
      background: #ffffff;
      border: 1.5px solid #e2e8f0;
      border-radius: 12px;
      padding: 10px 14px 12px;
      box-shadow: 0 2px 6px rgba(0, 0, 0, 0.03);
      display: flex;
      flex-direction: column;
      align-items: center;
    }

    .form-title {
      font-size: 11px;
      font-weight: 700;
      text-transform: uppercase;
      letter-spacing: 0.6px;
      color: #64748b;
      margin-bottom: 6px;
      display: flex;
      align-items: center;
      gap: 6px;
    }

    .form-title .tag {
      font-size: 9.5px;
      font-weight: 600;
      padding: 1px 6px;
      border-radius: 10px;
      background: #f1f5f9;
      color: #475569;
    }

    .equation-display {
      display: flex;
      align-items: center;
      justify-content: center;
      font-size: 22px;
      font-weight: 700;
      line-height: 1.2;
      min-height: 42px;
    }

    /* Math Tokens */
    .token {
      display: inline-flex;
      align-items: center;
      justify-content: center;
      padding: 2px 7px;
      border-radius: 6px;
      cursor: pointer;
      transition: background 0.15s, color 0.15s, box-shadow 0.15s, opacity 0.15s, border-color 0.15s;
      line-height: 1;
      font-family: inherit;
    }

    /* Base - Blue */
    .token-b {
      color: #1d4ed8;
      background: #eff6ff;
      border: 1.5px solid #93c5fd;
    }

    /* Exponent / Output - Coral/Orange */
    .token-y {
      color: #c2410c;
      background: #fff7ed;
      border: 1.5px solid #fdba74;
    }

    /* Value / Input - Teal */
    .token-x {
      color: #0f766e;
      background: #f0fdfa;
      border: 1.5px solid #5eead4;
    }

    /* Specific token placements */
    .exp-group {
      display: inline-flex;
      align-items: flex-start;
    }

    .token-exp {
      font-size: 15px;
      padding: 2px 5px;
      transform: translateY(-8px);
      margin-left: 1px;
    }

    .token-sub {
      font-size: 14px;
      padding: 1px 5px;
      transform: translateY(7px);
      margin-left: 1px;
      margin-right: 1px;
    }

    .op {
      color: #64748b;
      margin: 0 4px;
      font-weight: 600;
      font-size: 20px;
    }

    .log-txt {
      color: #334155;
      font-weight: 700;
      font-size: 20px;
      letter-spacing: -0.2px;
    }

    /* Focused & Dimmed States */
    .dimmed {
      opacity: 0.22;
    }

    .token.focused {
      box-shadow: 0 0 0 2.5px currentColor;
    }

    /* Connector Flow Paths */
    .flow-line {
      fill: none;
      stroke-linecap: round;
      stroke-linejoin: round;
      transition: stroke-opacity 0.2s, stroke-width 0.2s;
    }

    .flow-bg-shadow {
      fill: none;
      stroke: #ffffff;
      stroke-width: 6;
      stroke-linecap: round;
      opacity: 0.85;
    }

    .flow-b { stroke: #2563eb; }
    .flow-y { stroke: #ea580c; }
    .flow-x { stroke: #0d9488; }

    /* Legend */
    .legend {
      display: flex;
      justify-content: center;
      gap: 8px;
      width: 100%;
      flex-wrap: wrap;
      margin-top: 2px;
    }

    .legend-item {
      display: inline-flex;
      align-items: center;
      gap: 5px;
      font-size: 11.5px;
      font-weight: 600;
      padding: 4px 9px;
      border-radius: 16px;
      cursor: pointer;
      border: 1px solid transparent;
      transition: opacity 0.15s, background 0.15s, border-color 0.15s, box-shadow 0.15s;
    }

    .legend-b { color: #1d4ed8; background: #eff6ff; border-color: #bfdbfe; }
    .legend-y { color: #c2410c; background: #fff7ed; border-color: #fed7aa; }
    .legend-x { color: #0f766e; background: #f0fdfa; border-color: #99f6e4; }

    .legend-item.focused {
      box-shadow: 0 0 0 2px currentColor;
    }

    .dot-indicator {
      width: 7px;
      height: 7px;
      border-radius: 50%;
      background: currentColor;
    }

    /* Mobile adjustments (< 360px) */
    @media (max-width: 360px) {
      .equation-display { font-size: 20px; }
      .token-exp { font-size: 13.5px; transform: translateY(-7px); }
      .token-sub { font-size: 13px; transform: translateY(6px); }
      .stage { gap: 32px; }
      .tab-btn { font-size: 11px; padding: 5px 3px; }
    }
  </style>
</head>
<body>

  <div class="converter-wrap">
    
    <div class="controls">
      <button class="tab-btn active" onclick="setPreset(0)">General</button>
      <button class="tab-btn" onclick="setPreset(1)">2⁵ = 32</button>
      <button class="tab-btn" onclick="setPreset(2)">10³ = 1000</button>
    </div>

    
    <div class="hint-bar" id="hintBar">Hover or tap any variable to trace its position</div>

    
    <div class="stage" id="stage">
      
      <svg class="svg-overlay" id="svgOverlay">
        <defs>
          <marker id="arrow-b" markerWidth="6" markerHeight="6" refX="4.5" refY="3" orient="auto">
            <path d="M0,0.8 L5.5,3 L0,5.2 Z" fill="#2563eb" />
          </marker>
          <marker id="arrow-y" markerWidth="6" markerHeight="6" refX="4.5" refY="3" orient="auto">
            <path d="M0,0.8 L5.5,3 L0,5.2 Z" fill="#ea580c" />
          </marker>
          <marker id="arrow-x" markerWidth="6" markerHeight="6" refX="4.5" refY="3" orient="auto">
            <path d="M0,0.8 L5.5,3 L0,5.2 Z" fill="#0d9488" />
          </marker>
        </defs>

        
        <path id="bg-path-b" class="flow-bg-shadow" />
        <path id="bg-path-y" class="flow-bg-shadow" />
        <path id="bg-path-x" class="flow-bg-shadow" />

        
        <path id="path-b" class="flow-line flow-b" stroke-width="2.5" marker-end="url(#arrow-b)" />
        <path id="path-y" class="flow-line flow-y" stroke-width="2.5" marker-end="url(#arrow-y)" />
        <path id="path-x" class="flow-line flow-x" stroke-width="2.5" marker-end="url(#arrow-x)" />
      </svg>

      
      <div class="form-card" id="card-exp">
        <div class="form-title">
          <span>Exponential Form</span>
          <span class="tag">Base ᵞ = Value</span>
        </div>
        <div class="equation-display">
          <div class="exp-group">
            <span class="token token-b" id="exp-b" data-role="b">b</span>
            <span class="token token-y token-exp" id="exp-y" data-role="y">y</span>
          </div>
          <span class="op">=</span>
          <span class="token token-x" id="exp-x" data-role="x">x</span>
        </div>
      </div>

      
      <div class="form-card" id="card-log">
        <div class="form-title">
          <span>Logarithmic Form</span>
          <span class="tag">logᵦ(Value) = Exponent</span>
        </div>
        <div class="equation-display">
          <span class="log-txt">log</span>
          <span class="token token-b token-sub" id="log-b" data-role="b">b</span>
          <span class="op" style="margin-right:2px">(</span>
          <span class="token token-x" id="log-x" data-role="x">x</span>
          <span class="op" style="margin-left:2px">)</span>
          <span class="op">=</span>
          <span class="token token-y" id="log-y" data-role="y">y</span>
        </div>
      </div>
    </div>

    
    <div class="legend">
      <div class="legend-item legend-b" data-role="b">
        <div class="dot-indicator"></div>
        <span>Base (<strong id="leg-b">b</strong>)</span>
      </div>
      <div class="legend-item legend-y" data-role="y">
        <div class="dot-indicator"></div>
        <span>Exponent (<strong id="leg-y">y</strong>)</span>
      </div>
      <div class="legend-item legend-x" data-role="x">
        <div class="dot-indicator"></div>
        <span>Value (<strong id="leg-x">x</strong>)</span>
      </div>
    </div>
  </div>

  <script>
    const presets = [
      { b: 'b', y: 'y', x: 'x' },
      { b: '2', y: '5', x: '32' },
      { b: '10', y: '3', x: '1000' }
    ];

    const hints = {
      b: "Base: The repeated multiplier → Subscript of log",
      y: "Exponent: The power → Output (result) of log",
      x: "Value: The calculated total → Input (argument) of log"
    };

    let currentPreset = 0;
    let activeHighlight = null;

    function updateConnectors() {
      const stage = document.getElementById('stage');
      if (!stage) return;
      const stageRect = stage.getBoundingClientRect();
      const roles = ['b', 'y', 'x'];

      roles.forEach(role => {
        const el1 = document.getElementById(`exp-${role}`);
        const el2 = document.getElementById(`log-${role}`);
        const path = document.getElementById(`path-${role}`);
        const bgPath = document.getElementById(`bg-path-${role}`);

        if (!el1 || !el2 || !path || !bgPath) return;

        const r1 = el1.getBoundingClientRect();
        const r2 = el2.getBoundingClientRect();

        // Source: bottom-center of top token
        const x1 = (r1.left + r1.width / 2) - stageRect.left;
        const y1 = r1.bottom - stageRect.top + 2;

        // Target: top-center of bottom token (stop slightly above for arrowhead)
        const x2 = (r2.left + r2.width / 2) - stageRect.left;
        const y2 = r2.top - stageRect.top - 5;

        // Vertical distance & control points for dynamic graceful Bezier curve
        const dy = Math.max(y2 - y1, 10);

        // Curvature bias based on role so paths do not collide
        let c1x = x1;
        let c1y = y1 + dy * 0.45;
        let c2x = x2;
        let c2y = y2 - dy * 0.45;

        if (role === 'b') {
          // Base arcs towards the left side
          c1x -= 12;
          c2x -= 12;
        } else if (role === 'x') {
          // Value arcs smoothly inwards
          c1x += 4;
          c2x -= 4;
        } else if (role === 'y') {
          // Exponent sweeps out across towards the right
          c1x += 16;
          c2x += 8;
        }

        const d = `M ${x1.toFixed(1)} ${y1.toFixed(1)} C ${c1x.toFixed(1)} ${c1y.toFixed(1)}, ${c2x.toFixed(1)} ${c2y.toFixed(1)}, ${x2.toFixed(1)} ${y2.toFixed(1)}`;
        path.setAttribute('d', d);
        bgPath.setAttribute('d', d);
      });
    }

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

      const data = presets[idx];
      ['b', 'y', 'x'].forEach(role => {
        document.getElementById(`exp-${role}`).textContent = data[role];
        document.getElementById(`log-${role}`).textContent = data[role];
        document.getElementById(`leg-${role}`).textContent = data[role];
      });

      // Recalculate arrow paths after DOM update
      requestAnimationFrame(() => {
        updateConnectors();
        setTimeout(updateConnectors, 50);
      });
    }

    function setHighlight(role) {
      activeHighlight = role;
      const roles = ['b', 'y', 'x'];
      const hintBar = document.getElementById('hintBar');

      // Update Hint text
      if (role && hints[role]) {
        hintBar.textContent = hints[role];
        hintBar.className = `hint-bar highlight-${role}`;
      } else {
        hintBar.textContent = 'Hover or tap any variable to trace its position';
        hintBar.className = 'hint-bar';
      }

      roles.forEach(r => {
        const isTarget = !role || r === role;
        const path = document.getElementById(`path-${r}`);
        const bgPath = document.getElementById(`bg-path-${r}`);
        const tokens = document.querySelectorAll(`[data-role="${r}"]`);

        if (path) {
          path.style.strokeOpacity = isTarget ? '1' : '0.12';
          path.style.strokeWidth = role && isTarget ? '3.5' : '2.5';
        }
        if (bgPath) {
          bgPath.style.opacity = isTarget ? '0.9' : '0.05';
          bgPath.style.strokeWidth = role && isTarget ? '7' : '5';
        }

        tokens.forEach(el => {
          el.classList.toggle('dimmed', !isTarget);
          if (role && isTarget) {
            el.classList.add('focused');
          } else {
            el.classList.remove('focused');
          }
        });
      });
    }

    // Attach interactive listeners
    document.querySelectorAll('[data-role]').forEach(el => {
      const role = el.getAttribute('data-role');
      el.addEventListener('mouseenter', () => setHighlight(role));
      el.addEventListener('mouseleave', () => {
        if (!activeHighlight || activeHighlight === role) {
          setHighlight(null);
        }
      });
      el.addEventListener('click', (e) => {
        e.stopPropagation();
        setHighlight(activeHighlight === role ? null : role);
      });
    });

    // Clear focus on backdrop click
    document.addEventListener('click', () => {
      setHighlight(null);
    });

    // Resize handlers
    window.addEventListener('resize', updateConnectors);
    window.addEventListener('load', () => {
      updateConnectors();
      setTimeout(updateConnectors, 100);
    });

    if ('ResizeObserver' in window) {
      new ResizeObserver(() => updateConnectors()).observe(document.getElementById('stage'));
    }

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

HSF.BF.B.5

Aligned learning resources