Question

equações exponenciais 4x=3√32 por favor fazer a contra para facilidade o entendimento

Answer 1

$4^{x} = \sqrt[3]{32}$

$2^{2x} = 32^{ \frac{1}{3} }$

$2^{2x} = 2^{ \frac{5.1}{3} }$

$2x= \frac{5}{3}$

$6x=5$

$x= \frac{5}{6}$

$S={ \frac{5}{6}$}

Answer 2

$4^{x}=\sqrt[3]{32}~~\Rightarrow~~(2^2)^{x}=\sqrt[3]{2^5}$

$2^{2x}=2^{\frac{5}{3}}~~\Rightarrow~~2x=\dfrac{5}{3}$

$6x=5~~\Rightarrow~~\boxed{x=\dfrac{5}{6}}$

PS: $\sqrt[c]{a^b}=a^{\frac{b}{c}}$

Verificação:

$4^{\frac{5}{6}}=\sqrt[3]{32}~~\Rightarrow~~(2^2)^{\frac{5}{6}}=\sqrt[3]{2^5}$

$2^{\frac{10}{6}}=\sqrt[3]{2^5}~~\Rightarrow~~2^{\frac{5}{3}}=\sqrt[3]{2^5}$