Which one grows faster asymptotically: $\log(\log^an)$ or $\log^a(\log n)$
Assuming $\log^a n$ means $\log n$, raised to the power $a$: 

Let $t = \log \log n$, then the first expression equals $t·a$, while the second expression equals $t^a$. For $a &gt; 1$ the latter grows faster, for $a &lt; 1$ the former is faster, and for $a = 1$ they are identical.