Question

If $\log (x+3)-\log (x-3)=1$ is $3\frac{m}{3}$, the value of $m$ will be

• A. $1$
• B. $2$
• C. $-1$
• D. $-2$

Answer 1

The correct option is B $2$

$\log (x+3)-\log (x-3)=1$

$\log (x+3)=1+\log (x-3)$

$\text{Assuming base 10}$

$\log (x+3)=\log 10+\log (x-3)$

$\log (x+3)=\log 10(x-3)$

$\text{Removing log}$

$x+3=10x-30$

$9x=33$

$x=\frac{33}{9}=\frac{11}{3}=3\frac{2}{3}$