Question

What is the logarithm of $27$ to the base $9$ is

• A. 3
• B. $\frac{3}{2}$
• C. $\frac{1}{2}$
• D. None of these

Answer 1

The correct option is B $\frac{3}{2}$

${\log }_{9}27=\frac{\log 27}{\log 9}$ ....(${\log }_{b}a=\frac{\log a}{\log b}$)

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