Question

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

• A. 24
• B. 18
• C. 12
• D. 4

Answer 1

The correct option is A 24

${\log }_{8}m+{\log }_8\frac{1}{6}=\frac{2}{3}$

$\Rightarrow {\log }_8\frac{m}{6}=\frac{2}{3}$

$\Rightarrow \frac{m}{6}=8^{\frac{2}{3}}$

$\Rightarrow m=6\times 2^2$

$\Rightarrow m=24$

Hence, A is the correct option.