Question

If ${\log }_{8}m+{\log }_8\frac{1}{6}=\frac{2}{3}$, then $m$ is equal to

• A. $12$
• B. $48$
• C. $18$
• D. $24$

Answer 1

Answer: (D)

$24$

Given, ${\log }_{8}m+{\log }_8\frac{1}{6}=\frac{2}{3}$
$\Rightarrow {\log }_8\frac{m}{6}=\frac{2}{3}$
$\Rightarrow \log \frac{m}{6}=\frac{2}{3}\log 8$
$\Rightarrow \log \frac{m}{6}=\log 4$
$\Rightarrow \frac{m}{6}=4$
$\Rightarrow m=24$