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

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$