Question

If $\log (x+3)-\log (x-3)=1$ and $x=m\frac{2}{3}$, then $m$ is equal to

• A. $2$
• B. $1$
• C. $3$
• D. $4$

Answer 1

The correct option is C $3$

Given, $\log (x+3)-\log (x-3)=1$
$\Rightarrow \log \frac{x+3}{x-3}=\log 10$ ($\log \frac{a}{b}=\log a-\log b$)

$\Rightarrow \frac{x+3}{x-3}=10$

$\Rightarrow x+3=10x-30$
$\Rightarrow x=3\frac{2}{3}$