How to show that ${(\ln n)}^{\ln n}=n^{\ln(\ln n)}$ How to show that $${(\ln n)}^{\ln n}=n^{\ln(\ln n)}$$
Attempt:
$y={(\ln n)}^{\ln n}$ then $\ln y=\ln n\ln(\ln n)$ what to do next? 

HINT
We have
$${(\ln n)}^{\ln n}=e^{\ln n\cdot \ln (\ln n)}=(e^{\ln n})^{\ln (\ln n)}$$
and recall that by definition $e^{\ln n}=n$.
