title: f(n)=n^log(n) complexity polynomial or exponential
body: <p>I'm trying to figure out whether <code>f(n)=n^(logb(n))</code> is in <code>Theta(n^k)</code> and therefore grows polynomial or in <code>Theta(k^n)</code> and therefore grows exponentially.</p>
  
  <p>First I tried to simplify the function:
  <code>f(n) = n^(logb(n)) = n^(log(n)/log(b)) = n^((1/log(b))*log(n))</code> and because <code>1/log(b)</code> is constant we get <code>f(n)=n^log(n)</code>.</p>
  
  <p>But now I'm stuck. My guess is that <code>f(n)</code> grows exponentially in <code>Theta(n^log(n))</code> or even hyper exponentially because the exponent <code>log(n)</code> is also growing.</p>