I am trying to understand how to prove that a polynomial will always grow faster than a logarithm.$\log n = o(n^\epsilon), \epsilon>0$Intuitively, it is obvious, and plugging in a few numbers always yields true, but how can I prove this?Maybe this can be done inductively (I would prefer this method if someone would explain it), but I attempted to prove through the use of derivatives and L'Hpital's rule, namely:$\lim_{n\rightarrow\infty}\frac{\log n}{n^\epsilon} = \lim_{n\rightarrow\infty}\frac{\frac{1}{n}}{\epsilon n^{\epsilon-1}}$ = 0Is this getting me in the right direction to prove that the upper bound of $\log n$ it is strictly less than $n^\epsilon$?
Show that $\log n = o(n^\epsilon)$
asymptotics