Question

If ${\log }_{8}m+{\log }_8\frac{1}{6}=\frac{2}{3}$, then the value of $m$ will be

• A. $24$
• B. $2$
• C. $8$
• D. $12$

Answer 1

The correct option is A $24$

${\log }_{8}m+{\log }_8\frac{1}{6}=\frac{2}{3}$
$\therefore {\log }_8(m\times \frac{1}{6})=\frac{2}{3}$
$\therefore m\times \frac{1}{6}=8^{\frac{2}{3}}={\left(2^3\right)}^{\frac{2}{3}}=4$
$\therefore m=4\times 6=24$