Calculating the limit of a function? I've been trying to calculate the limit of the following, as $x$ tends to $0$:
$$f(x) = \left(\frac{e^x-1}x\right)^{1/x}$$

I've tried writing it as $e$ raised to the power of its log, but I am unable to solve it. Any tips on how to proceed will be appreciated!
$\lim_{x \to 0}\left( \dfrac{e^x-1}x \right)^\frac1x=\lim_{x \to 0}\left( \dfrac{(1+x+\frac{x^2}2+o(x^2))-1}x \right)^\frac1x=\lim_{x \to 0}\left( {1+\frac{x}2+o(x)} \right)^\frac1x=\lim_{x \to 0}e^{\frac1x \ln\left( {1+\frac{x}2+o(x)} \right)}=\lim_{x \to 0}e^{\frac1x \left( {\frac{x}2+o(x)} \right)}=\sqrt e$
Hint: Take log and use Lopitale rule.