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+<title>Math.log — Ludic</title>
+<meta name="description" content="The natural logarithm of x.">
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+  <div class="crumbs"><a href="api.html">API Reference</a> <span>›</span> <a href="ns-math.html">Math</a> <span>›</span> <span class="here">Math.log</span></div>
+  <div class="item-head">
+    <span class="kind-badge kind-method">method</span>
+    <h1 id="top">Math.log</h1>
+  </div>
+  <code class="sig">Math.log(x) -&gt; fixed</code>
+  <div class="desc"><p>Returns the natural logarithm <code>ln(x)</code> for <code>x &gt; 0</code>, computed in Q16.16 from a deterministic integer <code>log₂</code> (bit-scan for the exponent, a short series for the mantissa) scaled by <code>ln 2</code> — bit-identical on every platform. It is the inverse of <code>Math.exp</code>: reach for it to turn multiplicative growth into a straight line — score-to-level curves, logarithmic difficulty, decibel-style volume. Non-positive inputs are out of domain and saturate to a large negative value rather than returning a meaningful number.</p></div>
+  
+  <div class="examples"><h2>Example</h2><pre data-lang="ludic">program Demo {
+  handler Step phase Update {
+    let level = Math.floor(Math.log(score))   # diminishing returns on score
+  }
+}</pre></div>
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