It is in P/Q form, right?

Let's suppose 0 < $\log_35$ = $\frac {p}{q}$ where p,q are co-prime positive integers $\Rightarrow$ $3^{\frac {p}{q}}= 5$ $\Rightarrow$ $3^{p} = 5^{q}$ (Impossible due to Fundamental Theorem of Arithmetic) $\Rightarrow$ $\log_35$ is an irrational number