The question:

Determine the limiting behaviour of $\displaystyle \frac{ln(x^3+1)}{ln(x^2+1)}$ as x -> infinity.

My attempt:

I noticed that both the numerator and denominator approach infinity, making the limit indeterminate. Thus, I tried using L'Hopitals rule. However, in doing so, I can't seem to get an answer even after several differentiations. It seems to constantly become 0/0. Am I attempting this the right way?

Thanks!