Question

$4^{2m}={\left(\sqrt{8}\right)}^2$

Find the value of $\frac{3}{m}$

Answer 1

$4^{2m}={\left(\sqrt{8}\right)}^2$
$\Rightarrow {\left(2^2\right)}^{2m}={\left({\left(2^3\right)}^{\frac{1}{2}}\right)}^2$
$\Rightarrow 2^{2\cdot 2m}={\left(2^{3\cdot \frac{1}{2}}\right)}^2$
$\Rightarrow 2^{4m}=\left(2^{\frac{3}{2}\cdot 2}\right)$
$\Rightarrow 2^{4m}=2^3$
$2^{4m}=2^3$
Now will have equation for m
$\Rightarrow 4m=3\Rightarrow m=\frac{3}{4}$