title: Asymptotic Complexity of Logarithms and Powers
body: <p>So, clearly, <code>log(n)</code> is <code>O(n)</code>.  But, what about <code>(log(n))^2</code>?  What about <code>sqrt(n)</code> or <code>log(n)</code>—what bounds what?</p>
  <p>There's a family of comparisons like this:</p>
  <pre><code>nᵃ   (vs.)   (log(n))ᵇ
  </code></pre>
  <p>I run into these comparisons a lot, and I've never come up with a good way to solve them.  Hints for tactics for solving the <em>general</em> case?</p>
  <hr />
  <p>[EDIT: I'm not talking about the computational complexity of calculating the values of these functions.  I'm talking about the functions themselves.  E.g., <code>f(n) = n</code> is an upper bound on <code>g(n) = log(n)</code> because <code>f(n) ≤ c g(n)</code> for <code>c = 1</code> and <code>n₀ &gt; 0</code>.]</p>