title: T(n)=2T(n−−√)+logn
body: <p>I am trying to find the time complexity for the recurrence: </p>
  
  <blockquote>
    <p>T(n) = 2T(n<sup>1/2</sup>) + log n</p>
  </blockquote>
  
  <p>I am pretty close to the solution, however, I have run into a roadblock. I need to solve:   </p>
  
  <blockquote>
    <p>n<sup>(1/2<sup>k</sup>)</sup> = 1</p>
  </blockquote>
  
  <p>for k to simplify my substitution pattern. I am not looking for answers to the recurrence, just a solution for <code>k</code>.</p>