sequences and series - prove that $n^epsilon$/log(n) goes to infinity without derivatives or functions

I'm looking for a way to prove that for every
$\displaystyle{\quad\epsilon\ >\ 0\,,\quad{n^{\epsilon} \over \log\left(\, n\,\right)} \to \infty,\quad}$ treating it only as a sequence, without using functions and derivatives.

Any help will be appreciated