Question

The logarithm of $27$ to the base $9$ is $\frac{3}{m}$. Then the value of $m$ is equal to

• A. $0$
• B. $2$
• C. $3$
• D. $6$

Answer 1

The correct option is B $2$

Since, ${\log }_{9}27=\frac{3}{m}$ ...(1)

Let ${\log }_{9}27=x$

Converting in exponential form,

$27=9^x$

$3^3=3^{2x}$

$x=\frac{3}{2}$ ...(2)

Comparing equations (1) and (2), we get

$m=2$