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## Homework Statement

Find the limit as x->0+ of (ln(x))^x

*The answer is 1*

## Homework Equations

l'Hôpital's rule

## The Attempt at a Solution

lim (ln(x))^x = 0^0

I took the ln of that quantity to bring down the x

lim = x*ln(ln(x))

lim = ln(ln(x)) / (1/x)

Then I used l'Hôpital's rule

1/(x*ln(x)/(1/x^2)

= 1/(x^3*ln(x))

I got stuck here. If I plug in zero I get 0^3 and a undefined answer in the denominator. Do I have to do l'Hôpital's rule on the bottom again?

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