I'm trying to solve $\lim\limits_{x \to \infty}\frac{\ln^{1000} x}{x^5}$ Here's what I get: $e^{\lim\limits_{x \to \infty}\ln{\frac{\ln^{1000}x}{x^5} }}$ Dropping the $e$ for ease, $\lim\limits_{x \to \infty} 1000\ln{(\ln{(x)})} - 5 \ln{x} $
Now I have $\infty - \infty$.. I know there must be a next step, but I don't know what it would be.