Question

(logb x)/(1 + logb a) =​

Answer 1

Answer:

$\ \ \tt \: log_{ab}(x)$

Step-by-step explanation:

Given:

$\\\tt \dfrac{ log_{b}(x) }{1 +log_{b}(a) }$

Using bas change rule:

$\ \ \tt log_{x}(y) = \dfrac{ logx }{ logy}$

The expression becomes:

$\\\tt \dfrac{ \dfrac{ logx}{ logb } }{1 + \dfrac{ loga}{ logb } } = \\\tt \dfrac{ log(x) }{ logb +log(a) }$

Using sum rule:

$\ \ \tt \: log(xy) = log(x) + log(y)$

The expression becomes:

$\ \ \tt \: \dfrac{ log(x) }{ logab }$

Once again by using base change rule, the final answer we get is:

$\ \ \tt \: log_{ab}(x)$