Question

If logarithm of $\frac{1}{81}$ to the base $27$ is $-\frac{m}{3}$, then the value of $m$ is equal to

• A. $1$
• B. $5$
• C. $7$
• D. $4$

Answer 1

The correct option is D $4$

${\log }_{27}\frac{1}{81}=x\text{In exponent form}\frac{1}{81}={27}^x\frac{1}{3^4}=3^{3x}{3}^{-4}=3^{3x}x=\frac{-4}{3}{\log }_{27}\frac{1}{81}=\frac{-4}{3}$