Question

If ${\log }_{16}8$ = $\frac{3}{m}$, then value of $m$ is equal to

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is D $4$

${\log }_{16}8=\frac{3}{m}$

$\therefore \frac{\log 8}{\log 16}=\frac{3}{m}$ ....(${\log }_{b}a=\frac{\log a}{\log b}$)

$\therefore \frac{\log 2^3}{\log 2^4}=\frac{3}{m}$ ...($\log a^b=a\log b$)

$\therefore \frac{3}{m}=\frac{3}{4}$ $\Rightarrow m=4$.