1. ## Limit Problem

Hi, I'm having trouble starting this problem. Someone suggested using L'Hospital's rule but I can't figure out how to apply that here. Anyway, here's the problem, any help would be appreciated. Thanks in advance.

Lim x-->0+

X ^ ( -1 / ln(x) )

2. take the natural log

$\lim_{x \to 0^{+}} \ln \Big(x^{\frac {\text{-}1}{ln(x)}}\Big) = \lim_{x \to 0^{+}} \frac {\text{-}1}{\ln(x)} \ln(x)$ $= \text{-}1$

therefore, $\lim_{x \to 0^{+}} x^{\frac {\text{-}1}{ln(x)}} = e^{-1} = \frac {1}{e}$

3. Take log of the expression.

EDIT: Tooooo slooow.