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The limit as $n$ approaches infinity of $n(a^{1/n}-1)$

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I need to know how to calculate this without using l'hospitals rule:

limit as $x$ approaches infinity of: $$x(a^{1/x}-1)$$

I saw that the answer is $\log(a)$, but I want to know how they got it.The book implies that I should be able to find it by just using algebraic manipulation and substitution.


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