Question

If log ab base a= x, then log ab base b=

Answer 1

HELLO......FRIEND!!

THE ANSWER IS HERE,

$= > \: log_{a}(ab) = x$

$= > \: log_{a}(a) + log_{a}(b) = x$

$= > \: 1 + log_{a}(b) = x$

$= > \: log_{a}(b) = x - 1$


Given that,

$= > \: log_{b}(ab)$

$= > \: log_{b}(a) + log_{b}(b)$


$= > \: \frac{1}{ log_{a}(b) } + 1$

$= > \: \frac{1}{x - 1} + 1$

$= > \: \frac{1 + x - 1}{x - 1}$


$= > \: \frac{x}{x - 1}$

:-)Hope it helps u.

Answer 2

Hi Friend !!!

====================

$log_{a}(ab) = x \\ \\ log_{a}(a) + log_{a}(b) = x \\ \\ 1 + log_{a}(b) = x \\ \\ log_{a}(b) = x - 1 \\ \\ \\ log_{b}(ab) \\ \\ = log_{b}(a) + log_{b}(b) = \frac{1}{ log_{a}(b) } + 1 \\ \\ = \frac{1}{x - 1} + 1$
=1+x-1/x-1

= x/x-1

Hope it helps u