Question

Solve for $x$ such that $4^{2{\log }_{2}x}=81$.

Answer 1

Now,

$4^{2{\log }_{2}x}=81$

or, $2^{4{\log }_{2}x}=81$

or, $2^{{\log }_2{x}^4}=81$

or, $x^4=81$ [ Since ${\log }_{a}a=1$ for $a>0$]

or, $x^4=3^{4}1$

or, $x=3$