Question

If $\log (a+b)=\log a+\log b$, then write $a$ in terms of $b$ is

• A. $\frac{1-b}{b}$
• B. $\frac{1+b}{b}$
• C. $\frac{b}{b-1}$
• D. $\frac{b-1}{b}$

Answer 1

The correct option is C $\frac{b}{b-1}$

We have,

$\begin{array}{c}\log \left(a+b\right)=\log a+\log b\\ \log \left(a+b\right)=\log ab\\ a+b=ab\\ ab-a=b\\ a=\frac{b}{b-1}\end{array}$

Option $C$ is correct answer.