I am interested in solving logarithmic expressions but I cannot do this.
what does this expression simplify to?
$n^{\log \log n/\log n}$
I am interested in solving logarithmic expressions but I cannot do this.
what does this expression simplify to?
$n^{\log \log n/\log n}$
Assuming $n \neq 1$, and let
$y = n^{\log \log n/\log n}$
$ \log y = \frac{\log \log n}{\log n} \log n = \log \log n$
$ \Rightarrow y = \log n$
(Spelling correction done)
Note that $n = e^{\log n}$, so $n^x = e^{x\log n}$.
Then $n^{\log\log n / \log n} = e^{(\log\log n / \log n)\cdot\log n} = e^{\log\log n}$.
$e^{\log \log n} = \log n$.