title: Solving power towers
body: <pre><code>a=2^Power[10^6, 10^9] 3^Power[4^9, 7^5]
  TwoTower[n_] := Nest[2^# &amp;, 1, n]
  </code></pre>
  
  <p>What's the smallest <code>n</code> such that <code>TwoTower[n]&gt;a</code>? This <a href="http://www.quora.com/How-can-I-compare-two-very-large-numbers" rel="nofollow">question</a> had a pen-and-paper answer on Quora, is there a way to use Mathematica here?</p>