Question

If ${\log }_a\left(ab\right)$ = x then evaluate ${\log }_b\left(ab\right)$ in terms of x

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

${\log }_a\left(ab\right)$ = x

${\log }_{a}a$ + ${\log }_{a}b$ = x

We know, ${\log }_{a}a$ = 1

1 + ${\log }_{a}b$ = x

${\log }_{a}b$ = x - 1; ${\log }_{b}a$ = $\frac{1}{x-1}$

${\log }_b\left(ab\right)$ = ${\log }_{b}a$ + ${\log }_{b}b$ = $\frac{1}{x-1}$ + 1 = $\frac{1+x-1}{x-1}$ = $\frac{x}{x-1}$