How $\text{Log}_a(Z)$ = $\frac{\text{Log}(Z)}{\text{Log} (a)}$ ? where $a,z \in \mathbb C$.

Question

Can anyone tell me how $\ \text{Log}_a(Z)$ = $\frac{\ \text{Log}(Z)}{\ \text{Log} a}$ where $a,z \in \mathbb C$ ?

I was told that the right hand side is not the definition of the left hand side. It can be deduced from the left hand side.

Can anyone please help me to understand?

Answer 1

Hint: Let $\log_az=y \implies a^y=z.$ Then take $\log$ on both sides.