calculus - Prove that $lim limits_{xto infty}e^{frac{ln(x)}{x}}=1$

How to prove that $\lim \limits_{x\to \infty}e^{\frac{\ln(x)}{x}}=1$?

I know that $x$ grows much faster to infinity then $\ln(x)$, therefore the limit equivalent to $e^0 = 1$

but that's not a rigorous proof.

Answer

$$\lim_{x \to \infty}\frac{\ln{x}}{x}=\lim_{x \to \infty}\frac{1}{x}=0$$

by L Hopital's Rule