title: How to prove logarithmic complexity
body: <pre><code>for (int i = 1; i &lt; N; i *= 2) { ... }
  </code></pre>
  
  <p>Things like that are the signatures of logarithmic complexity.</p>
  
  <p>But how get log(N)?</p>
  
  <p>Could you give mathematical evidence?</p>