Convergence of Geometric series with logrithmic power

Question

I have been having trouble understanding where the convergence conditions for this series came from. The series is: $$\sum_{n=1}^{\infty} a^{ \log(n)} $$ And this is supposed to converge when $\log(|a|) < -1$, but I don't see where this condition came from.

Answer 1

$$\sum_{n=1}^{\infty}a^{\log(n)}=\sum_{n=1}^{\infty}n^{\log(a)}$$

Clearly, this only converges for when $\log(a)<-1\implies 0<a<\frac{1}{e}$, assuming $a$ is real.