I am trying to find $\lim_{x \rightarrow0} (1-3 \cdot x)^{\frac{1}{x}}$
I thought about finding the limit of
$(1-3 \cdot x)^{\frac{1}{x}}= e^{\frac{\ln(1-3 \cdot x)}{x}}$
But that only works if $e^{\frac{\ln(1-3 \cdot x)}{x}}$ is continuous at $x=0$, which as far as I understand it is not. Am I right about that? And if I am, how do I find the limit?
Thanks!