The limit $lim_{nto infty}{na^n}=0$

Let $a\in [0,1)$. I want to show that $$\lim_{n\to \infty}{na^n}=0$$

My try : $$na^n={n\over e^{-(\log{a})n}}$$ and the limit is $${+\infty\over +\infty}$$
Hence by l'Hopital's rule we have that
$$\lim_{n\to \infty}{1\over -(\log{a})e^{-(\log{a})n}}={1\over -\infty}=0$$

Is there any other way to compute this limit ? thanks!