title: What is wrong with this reasoning to determine the upper bound?
body: <p>I was given a question in the algorithm class</p>
  
  <pre><code>is 2^{2n} upper bounded by  O(3^n)?
  </code></pre>
  
  <p>Now clear 2^2n is 4^n, and 4^n can't be upper bounded by 3^n.</p>
  
  <p>However if I take log on both sides</p>
  
  <pre><code>On LHS I get 2n
  On RHS I get kn (where k is some constant)
  </code></pre>
  
  <p>2n can be upper bounded by kn, so it is contradicting of the more obvious claim above. What I am doing wrong in this reasoning?</p>