Question

The value of $\log ab-\log \left|b\right|$ is equal to

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

Answer 1

Answer: (B)

$\log \left|a\right|$

Let $k=\log ab-\log \left|b\right|$
Case 1:
If $b>0$, then $\left|b\right|=b$
$k=\log ab-\log \left|b\right|$
$\Rightarrow k=\log a+\log b-\log b$
$\Rightarrow k=\log a$
Case 2:
If $b<0$, then $\left|b\right|=-b$
$k=\log ab-\log (-b)$
$\Rightarrow k=\log \left(\frac{ab}{-b}\right)$
$\Rightarrow k=\log (-a)$
From case 1 & case 2:
$k=\log \left|a\right|$
Ans: B