Math Help - Limit

1. Limit

Prove that $\lim_{x\rightarrow\infty}\frac {\ln (x+1)}{\ln x}=1$.

2. Originally Posted by james_bond
Prove that $\lim_{x\rightarrow\infty}\frac {\ln (x+1)}{\ln x}=1$.
Use L'Hopital's rule

$\lim_{x\rightarrow\infty}\frac {\ln (x+1)}{\ln x}= \lim_{x\rightarrow\infty}\frac {\frac{1}{1+x}}{\frac{1}{x}}= \lim_{x\rightarrow\infty}\frac {x}{x+1}=1$