Question

prove that log x to the base ab = (log a X)(log b X)/log a X + log b X

Answer 1

Hope this helps you.......

Answer 2

Answer and explanation:

To prove : $\log_{ab}x=\frac{(\log_a x)(\log_b x)}{\log_a x+\log_b x}$

Proof :

Taking RHS,

$\frac{(\log_a x)(\log_b x)}{\log_a x+\log_b x}$

$=\frac{(\log_a x)(\log_b x)}{\frac{1}{\log_x a}+\frac{1}{\log_x b}}$

$=\frac{(\log_a x)(\log_b x)}{\frac{\log_x a+\log_x b}{(\log_x a)(\log_x b)}}$

$=\frac{(\log_a x)(\log_b x)(\log_x a)(\log_x b)}{\log_x a+\log_x b}$

$=\frac{1}{\log_x a+\log_x b}$

$=\frac{1}{\log_x (ab)}$

$=\log_{ab}x$

= LHS

Hence proved.