How to solve $\lim_{x \to \ 0^+} (\mid \ln(x) \mid)^{\frac{1}{x}}$ I want to solve $$\lim_{x \to \ 0^+} (\mid \ln(x) \mid)^{\frac{1}{x}}$$.

Thanks for help.
Hint: $$\left(|\ln(x)| \right)^{\frac{1}{x}}=\exp\left(\dfrac{1}{x}\ln(|\ln(x)|) \right)$$
One can compute this limit as a composition of well known limits.
$\forall x$ such as $ 0&lt;x&lt;\dfrac{1}{e²}$, $(\mid \ln(x) \mid)^{1/x}&gt;2^{1/x}$

And $\lim_{x \to \ 0^+} 2^{1/x}=+\infty$ ...