# Limit of x^((x^x)-1) as x->0

1. Jan 26, 2013

### tsuwal

1. The problem statement, all variables and given/known data
Limit of x^((x^x)-1) as x->0

2. Relevant equations
Lim x^x=1
x->0

3. The attempt at a solution
it's an 0^0 indetermination so I tried to solve it the usual way, by first calculating the limit of log(x)*(x^x-1) as x->0 with L'hopital's rule. I got e^0=1 confirmed by Wolfram. However, the using L'hopitals rule on this limit is not very practical, is there a better soluction?

2. Jan 26, 2013

### Zondrina

Suppose you let y = x^((x^x)-1), what is ln(y) = ?

3. Jan 26, 2013

### tsuwal

I would get the same limit log(x)*(x^x-1) as x->0 but solving this by L'hopital's rule takes a while or is it the fastest way?

4. Jan 26, 2013

### Zondrina

Oh whoops, I read too quickly. Yeah I don't see how you would do this without LH otherwise.

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