title: Proof n^2 - 4n = Big-Theta(2^n)
body: <p>I should prove or disprove the equation<br>
      n^2 - 4n = Big-Theta(2^n)</p>
  
  <p>As far as i know i need to prove the following two equations:</p>
  
  <pre><code>f = O(g)
  g = O(f)
  </code></pre>
  
  <p>I started to solve f = O(g)</p>
  
  <pre><code>n^2 - 4n = c * 2^n // use log
  2log(n) - log(4n) = log(c) * n * log(2)
  2log(n) - (log(4) + log(n)) = log(c) * n //log(2) at base 2 is 1
  </code></pre>
  
  <p>But how do i continue from here on?</p>