Question

Calcule o valor de x na equação a seguir:

$x^{x^3} = 3$

Answer 1

Resposta:

$x=\sqrt[3]{3}$

Explicação passo a passo:

Primeiro vamos chamar o expoente x³ de y:

$x^{3} = y\\\\\\\\x=\sqrt[3]{y}\\ \\x^{y}=3\\\sqrt[3]{y}^{y}=3\\{y^{\frac{y}{3} }}^{3} = 3^{3}\\y^y=3^3\\y=3\\\\x=\sqrt[3]{3}$

Answer 2

$\displaystyle \sf x^{x^{3}} = 3 \\\\\ \text{Fa{\c c}amos }: \\\\ x^3 = y \to x=\sqrt[3]{\sf y} \\\\ \text{Da{\'i}} : \\\\ \left(\sqrt[3]{\sf y}\right)^{\left(\sqrt[3]{\sf y}\right)^{3}} = 3 \\\\ \left(\sqrt[3]{\sf y}\right)^{y} = 3 \\\\ \left(y^{y}\right)^{\frac{1}{3}} = 3 \\\\ \text{elevando ambos os lados por 3} : \\\\ y^y = 3^3 \\\\ y = 3 \\\\ Portanto :\\\\ x = \sqrt[3]{\sf y} \\\\ \huge\boxed{\ \sf x = \sqrt[3]{3} \ }\checkmark$