How to find this limit? L’hopital’s rule is never-ending

Question

I have the following limit
$$
\lim_{x\to\infty}\frac{-7^x}{(\ln11-\ln7)\cdot11^x}$$
Graphing gives me $0$ but plugging it in gives infinity over infinity.

I then tried L'Hôpital's rule and it seems to fall into a never ending loop. I can't seem to simplify this – what would be the best way to find the limit?

Edit: would like to clarify I want to know how to find it algebraically

Answer 1

You can write the expression as $-\left(\ln \frac{11}{7}\right)^{-1} \left(\frac{1}{(11/7)}\right)^x$, which goes to zero as $x \rightarrow \infty$