Question

The value of $\log ab-\log \left|b\right|$ =

• A. $\log a$
• B. $\log \left|a\right|$
• C. $-\log a$
• D. None of these

Answer 1

The correct option is B $\log \left|a\right|$

$\log ab$ is defined if ab > 0 or a and b have the same sign.

Case (i): a, b > 0:

$\Rightarrow \log ab-\log \left|b\right|=\log a+\log b-\log b=\log a$...(i)

Case (ii): a, b < 0:

$\Rightarrow \log ab-\log \left|b\right|=\log (-a)+\log (-b)-\log (-b)=\log (-a)$...(ii)

From Eqs. (i) and (ii), we have $\log ab-\log \left|b\right|=log\left|a\right|$.