Question

raiz quadrada de 2^x = 1/raiz cubica de 16​

Answer 1

Resposta:

S = {-8/3}

Explicação passo-a-passo:

$\sqrt{ {2}^{x} } = \frac{1}{ \sqrt[3]{16} } \\ \sqrt{ {2}^{x} } \times \sqrt[3]{16} = 1 \\ \sqrt[6]{( {2}^{x})^{3} } \times \sqrt[6]{ {16}^{2} } = 1 \\ \sqrt[6]{ {2}^{3x} \times 256} = 1 \\ {( \sqrt[6]{256. {2}^{3x} }) }^{6} = {1}^{6} \\ 256. {2}^{3x} = 1 \\ {2}^{8} . {2}^{3x} = 1 \\ {2}^{3x + 8} = {2}^{0} \\ 3x + 8 = 0 \\ 3x = - 8 \\ x = - \frac{8}{3}$

Verificação:

$\sqrt{ {2}^{x} } = \frac{1}{ \sqrt[3]{16} } \\ \sqrt{ {2}^{ - \frac{8}{3} } } = \frac{1}{ \sqrt[3]{16} } \\ \sqrt{ {2}^{ - \frac{8}{3} } } . \sqrt[3]{16} = 1 \\ {2}^{ - \frac{8}{3} \div 2} . {2}^{ \frac{4}{3} } = 1 \\ {2}^{ - \frac{8}{3} \times \frac{1}{2} } . {2}^{ \frac{4}{3} } = 1 \\ {2}^{ - \frac{4}{3} } . {2}^{ \frac{4}{3} } = 1 \\ {2}^{ - \frac{4}{3} + \frac{4}{3} } = 1 \\ {2}^{0} = 1 \\ 1 = 1 \: (verdadeiro)$