garnirativ8

## Answered question

2022-10-03

lHopitals $\underset{x\to \mathrm{\infty }}{lim}\phantom{\rule{thickmathspace}{0ex}}\left(\mathrm{ln}x{\right)}^{3x}$?
Okay, so what do I do with that power? I need to rewrite the term as fractions. How?
If it was the inner function that's in the power of something: $\mathrm{ln}{x}^{\frac{1}{3x}}$ then I'd just simply rewritten it as $\frac{1}{3x}\cdot \mathrm{ln}x=\frac{\mathrm{ln}x}{3x}$

### Answer & Explanation

beshrewd6g

Beginner2022-10-04Added 12 answers

Why do you hant to use l'hopital ?
$\left(\mathrm{ln}x{\right)}^{3x}={e}^{3x\mathrm{ln}\left(\mathrm{ln}\left(x\right)\right)}$
and since $3x\mathrm{ln}\left(\mathrm{ln}\left(x\right)\right)\underset{x\to \mathrm{\infty }}{⟶}\mathrm{\infty }$,
$\underset{x\to \mathrm{\infty }}{lim}\left(\mathrm{ln}x{\right)}^{3x}=\mathrm{\infty }.$

ter3k4w8x

Beginner2022-10-05Added 4 answers

That isn't a indeterminate form. $\mathrm{ln}x\to \mathrm{\infty }$ as $x\to \mathrm{\infty }$. So does $3x$.
${\mathrm{\infty }}^{\mathrm{\infty }}=\mathrm{\infty }$
The power law for limits comes into play and we get our limit.

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