I am having difficulty understanding how this follows.
$(\log n)^{ (\log n) } = 2^{(\log n)(\log (\log n))} = n^{\log \log n}$
Which logarithmic identities are used to go through each equality?
e.g. how do you first go from
$(\log n)^{ (\log n) } = 2^{(\log n)(\log (\log n))}$
and then to
$2^{(\log n)(\log (\log n))} = n^{\log \log n}$
(The log base must be 2 or else this equality won't hold)