Here's the question you clicked on:
oksanaekjord
solve lim x->inf (ln x)^(1/x)
\[\lim_{x\rightarrow\infty}(\ln x)^{\frac 1x}=1\]
start by taking the log get \[\frac{1}{x}\ln(\ln(x))=\frac{\ln(\ln(x))}{x}\]
now that limit is pretty clearly 0, since log grows much slower than \(x\) and the log of the log grows amazingly slowly since that limit is 0, and it is the limit of the log, you get \(e^0=1\) and the limit of your original question