Question

equação exponencial



$\sqrt{3} ^{x} =9^\frac{1}{2}$

Answer 1

Oi!

$\sqrt{3^x} = {9}^{\frac{1}{2}} \\ {3}^{\frac{x}{2}} = {9}^{\frac{1}{2}} \\ {3}^{\frac{x}{2}} = {(3^3)}^{\frac{1}{2}} \\ {3}^{\frac{x}{2}} = {3}^{\frac{3}{2}} \\ \frac{x}{2} = \frac{3}{2}\\ \boxed{x = 3}$

Propriedade:
$\boxed{ \sqrt[n]{a^m} = {a}^{\frac{m}{n}}}$

Bona estudos!