Computing the limit of $(\log n)^{0.5}/\log n^{0.5}$

Question

$$\lim\limits_{n\to\infty}\frac{(\log n)^{0.5}}{\log n^{0.5}}$$

I'm really not sure where to begin with this. Are there some basic laws of logs that I should apply first?

Answer 1

$$\lim\limits_{n\to\infty}\frac{(\log n)^{\frac12}}{\log n^{\frac12}}=\lim\limits_{n\to\infty}\frac{\sqrt{\log n}}{\frac12\log n}$$ $$=2\lim\limits_{n\to\infty}\frac{\sqrt{\log n}}{\log n}=2\lim\limits_{n\to\infty}\frac{1}{\sqrt{\log n}}=0$$