Prove little-o example

Question

Let $f(x)=\log x$, and $g(x)=x^i$, where $0<i<1$. How can I correctly proof that $f(x)=o(g(x))$?

Try 1: By the definition of little-o, a function is little-o of other function if $|f(x)|\leq C|g(x)|$ for all $x>m$. I was thinking of choosing $i$ to be 1, then proof that $\log x = o(x)$ but I am not sure if this is correct.

Answer 1

It is usually enough to show that $\frac{f}{g} \to_n 0$ to show $o(▪)$