- #1

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## Homework Statement

here it is:

the teacher suggeste to solve it with de l'hopital, however it is not necessary

## \displaystyle \lim x \to +\infty\ (\frac{a^x -1}{x(a-1)})^\frac{1}{x}##

with ## a>0## , ##a≠1##

## The Attempt at a Solution

the indeterminate formula is ## (\frac{\infty}{\infty})^0 ##

but i thought of changing the variable ##x \to \infty## to ##z \to 0##

such that i have the known:

## \frac{(a^{\frac{1}{t}}-1)}{\frac{1}{t}} = log(a)##

so i obtain:

##(\frac{log(a)}{a-1})^{+\infty} ##

but i don't know how to go on..