title: Proving big O of statement
body: <p>I am having a hard time proving that <code>n^k</code> is <code>O(2^n)</code> for all <code>k</code>. I tried taking <code>lg2</code> of both sides and have <code>k*lgn=n</code>, but this is wrong. I am not sure how else I can prove this.</p>