Question

The logarithm form of $(81{)}^{\frac{3}{4}}=27$ is ${\log }_{81}27=\frac{3}{m}$. Then value of $m$ is equal to

• A. $2$
• B. $0$
• C. $4$
• D. $3$

Answer 1

Answer: (C)

$4$

Given, ${\log }_{81}27=\frac{3}{m}$ ...(1)

Now, $(81{)}^{\frac{3}{4}}=27$

Converting in logarithm form, we can write

${\log }_{81}27=\frac{3}{4}$. ...(2)

From (1) and (2), we get

$\frac{3}{m}=\frac{3}{4}$

$\therefore m=4$