L' Hopital's Rule for non fraction.

**jjtjp** · Apr 6th 2013, 04:46 PM

The problems states, Evaluate the limit using L'Hopital's rule:
$\lim_{x \to \0}(1-5x)^{\frac{1}{x}}$

Can someone walk me through how to make this into a fraction so that I can attempt the rule? Thanks!

**hollywood** · Apr 6th 2013, 09:05 PM

You take the logarithm: find $\lim_{x\to{0}}}\ln\left((1-5x)^{\frac{1}{x}}\right)=\lim_{x\to{0}}}\frac{\ln( 1-5x)}{x}$ and if the answer is L, the answer to the original problem is $e^L$ .

- Hollywood

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