sequences and series - Evaluation $lim_{nto infty}frac{n^{log m}}{m^{log n}}$

Evaluate where $m>1$ is constant

$$\lim_{n\to \infty}\frac{n^{\log m}}{m^{\log n}}$$

I tried to use L'Hopital rule but it didn't work.

I have no idea how to evaluate this limit. Can you help me with that?

Answer

The sequence is constant. Take the logarithm of each part and compare.