Question

If ${\log }_a\frac{1}{4}=-\frac{2}{3}$, then $a$ is equal to_____

• A. $8$
• B. $5$
• C. $7$
• D. $6$

Answer 1

Answer: (A)

$8$

${\log }_a\left(\frac{1}{4}\right)=-\frac{2}{3}$

$\Rightarrow \frac{1}{4}=a^{-2/3}$

Taking exponent/power $-3/2$ both sides, we get

$\Rightarrow a^{-\frac{2}{3}\times -\frac{3}{2}}={\left(\frac{1}{4}\right)}^{-\frac{3}{2}}$

$\Rightarrow a={64}^{\frac{1}{2}}=8$

Hence, A is the correct option.