I haven't practiced limits for years, now I need them to solve an exercise and I don't know whether I have come up with the right solution.
$$\lim_{n \to \infty}{\frac{n^a}{\log\left(\left| \log(n^a)\right|\right)}}$$
where $a$ is a fixed constant.
Since I have the form $\frac{\infty}{\infty}$, I apply the De L'Hopital theorem, so I derive both numerator and denominator, so:
$$\lim_{n \to \infty}{\frac{an^{a-1}}{\frac{a}{n\log(n^a)}}} = \lim_{n \to \infty}{n\log(n^a)} = \lim_{n \to \infty}{a n\log(n)} = \infty$$
Can you please give me any feedback?