Q:

Find the following limits. $\lim_{x\to e^+} (\ln x)^{\frac{1}{x-e}}$

Find the following limits.
$$\lim_{x\to e^+} (\ln x)^{\frac{1}{x-e}}$$
I need some clues or hints to get me started. I can't even make a step. Thanks stack!
I think I can bring the limit up to the power, since ln x is continuous near e. 

A:

Write $y = (\ln(x))^{1\over x - e}$. Then $\ln(y) = {\ln(\ln(x))\over {x - e}}$
You are now in an $0\cdot \infty$ situation. What can you do?

