Question

These are numeric entry type questions.
If ${\log }_{64}{x}^4=1\frac{1}{3}$, then the value of ${\log }_4{x}^2$ is______

Answer 1

Answer: 2

Given, ${\log }_{64}{x}^4=1\frac{1}{3}$
${\log }_{64}{x}^4=\frac{4}{3}$
$x^{\frac{4}{3}}=(4{)}^{\frac{4}{3}}$
$x^4=4^4$
$x=4$
${\log }_4{x}^2={\log }_4{4}^2=2\times 1=2$