How do i solve this limit using L'Hopital Rule?

[ParveshD.Singh]

 

[skeeter]

let [MATH]y = \lim_{x \to \infty} \left(\dfrac{\ln{x}}{x}\right)^{1/\ln{x}}[/MATH]
[MATH]\ln{y} = \lim_{x \to \infty} \dfrac{1}{\ln{x}} \ln\left(\dfrac{\ln{x}}{x}\right)[/MATH]
[MATH]\ln{y} = \lim_{x \to \infty} \dfrac{1}{\ln{x}} \cdot \left[\ln(\ln{x}) - \ln{x}\right][/MATH]
see what you can do from here ...