How to calculate $\lim_{n \to \infty} \frac{(\ln(n))^n}{(\ln(n+1))^{n+1}}$ How would I solve the following limit
$\lim_{n \to \infty} \frac{(\ln(n))^n}{(\ln(n+1))^{n+1}}$
Is there an intuitive way of solving it?
I have no clue on how to start. Any help would be appreciated.

$\lim_{n \to \infty} \frac{(\ln(n))^n}{(\ln(n+1))^{n+1}}\\
\lim_{n \to \infty} \left(\frac{\ln(n)}{\ln(n+1)}\right)^n\left(\lim_{n \to \infty}\frac 1{\ln(n+1)}\right)
$
$\left(\frac{\ln(n)}{\ln(n+1)}\right)<1$ for all $n>0$
$\lim_{n \to \infty}\frac 1{\ln(n+1)} = 0$
