Question

The value of ${\log }_2\frac{1}{8}$ is equal to

• A. $-3$
• B. $3$
• C. $\frac{1}{3}$
• D. $-\frac{1}{3}$

Answer 1

The correct option is A $-3$

${\log }_2\frac{1}{8}=\frac{\log \frac{1}{8}}{\log 2}$ ....(since ${\log }_{b}a=\frac{\log a}{\log b}$)
$\therefore \frac{\log 2^{-3}}{\log 2}=-3$ ...($\log a^b=b\log a$)