Question

The value of ${log}_3\left(27\sqrt{3}\right)$ is

• A. $\frac{1}{2}$
• B. $\frac{3}{2}$
• C. $\frac{5}{2}$
• D. $\frac{7}{2}$

Answer 1

The correct option is D $\frac{7}{2}$

${\log }_3\left(27\sqrt{3}\right)$

$={\log }_3(3^3\times 3^{\frac{1}{2}})$

$={\log }_3\left(3^{3+\frac{1}{2}}\right)$

$={\log }_3{3}^{\frac{7}{2}}$

$=\frac{7}{2}{\log }_{3}3$ since $\log a^m=m\log a$

$=\frac{7}{2}$ since ${\log }_{a}a=1$