Limits involving indeterminate forms I am trying to find $\lim_{x \to \infty} (\ln x)^{1/x}$ and I have gotten it to $\lim\limits_{x \to \infty} \frac{1}{x \ln x}$.
The answer is $1$ and I just can't figure out why.

Hint: if $x\gt 1$, then $(\ln x)^{1/x}=\exp\left(\frac{\ln(\ln x)}{x}\right)$
The behaviour of $\frac{\ln(\ln x)}{x}$ for large $x$ can be found in various ways, for example by using L'Hospital's Rule. Then use the cotinuity of the function $\exp(t)$.
