Question

Evaluate:

$\frac{\log \sqrt{8}}{\log 8}$

• A. $\frac{1}{\sqrt{8}}$
• B. $\frac{1}{4}$
• C. $\frac{1}{2}$
• D. $\frac{1}{8}$

Answer 1

The correct option is C $\frac{1}{2}$

$\frac{\log \sqrt{8}}{\log 8}={\log }_8\sqrt{8}$ using $\frac{\log a}{\log b}={\log }_{b}a$

$={\log }_8{8}^{\frac{1}{2}}$

$=\frac{1}{2}{\log }_{8}8$ using $\log a^m=m\log a$

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