Identity (logarithms)

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!

• Did you mean $\frac{\log_{a}X\times\log_{b}X}{\log_{a}X+\log_{b}X}$? – barak manos Dec 4 '16 at 16:44
• yes! Solved! Thanks! – Garry Boch Dec 4 '16 at 17:12

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