Question

The value of $\frac{log8}{log\sqrt{2}}$ is

• A. 2
• B. 4
• C. 5
• D. 6

Answer 1

The correct option is D 6

$\frac{\log 8}{\log \sqrt{2}}$

$={\log }_{\sqrt{2}}8$ since $\frac{\log a}{\log b}={\log }_{b}a$

$={\log }_{2^{\frac{1}{2}}}{2}^3$

$=\frac{3}{\frac{1}{2}}{\log }_{2}2$ since ${\log }_{a^n}{a}^m=\frac{m}{n}{\log }_{a}a$

$=6$ since ${\log }_{a}a=1$