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 : Take log on both sides 

$${(\ln n)}^{\ln n}=n^{\ln(\ln n)}$$
  Taking log gives 
  $$ \ln\left({(\ln n)}^{\ln n}\right) =\ln\left(n^{\ln(\ln n)}\right)$$
  $$ \ln({n})( \ln(\ln(n))= {\ln(\ln n)} \ln(n)$$

