Limit of $\underset{n\to \infty }{\text{lim}}\frac{\ln (n+1)}{\ln (n)}$ without L'Hôpital I intuitively understand that the limit goes to 1 and I can solve with L'Hôpital but I can't without it.
I tried to call it equal to y and rise both sides to the base e but doesn't seems to work.
$\underset{n\to \infty }{\text{lim}}\frac{\ln (n+1)}{\ln (n)}$

Hint: $\displaystyle\log(n+1)=\log\left(n\left(1+\frac1n\right)\right)=\log(n)+\log\left(1+\frac1n\right)$
