If $\sqrt{8}=2^x,$ then find the value of $x.$

The correct option is C $\frac{3}{2}$
Given, $\sqrt{8}=2^x.$

$\text{LHS}=\sqrt{8}=8^{\frac{1}{2}}=(2\times 2\times 2{)}^{\frac{1}{2}}=(2^3{)}^{\frac{1}{2}}=2^{3\times \frac{1}{2}}=2^{\frac{3}{2}}\because ((a^m{)}^n=a^{mn})$

$\therefore 2^{\frac{3}{2}}=\text{RHS}=2^x$

Equal powers with equal bases have equal exponents.
$\therefore x=\frac{3}{2}$