[Math] Prove that $\log_9 15$ is irrational

Question

Im having trouble with the following proof… Ill post what I have completed so far..

Prove that $\log_915$ is irrational.

Ill attempt by contradiction assuming $\log_915$ is rational.

So,

$\log_915 = \frac ab$

$15 = 9^{\frac ab}$

$15^b = 9^a$
(This is where I'm getting stuck)

Any hints/tips/advice would be great. Thanks

Answer 1

$a$ and $b$ are positive integers. $15^b$ and $9^a$ are positive integers. $5$ definitely does not divide $9^a$, so what must $b$ be?