Identity (logarithms)

Question

There is a simple question for identity:

$\log_{ab}X = \frac{\log(a)X \times \log(b)X}{\log(a)X + \log(b)X}$

To proof, I goes for $ab$ base for right, but seems Im wrong.

Can anyone help?

Thank you!

Answer 1

Hint:

$$\log_r s=\frac1{\log_s r}$$