Question

log de 2 raiz de 2 na base x igual a 3?

Answer 1

Resposta:

x=√2

Explicação passo-a-passo:

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$log_{x}(2 \sqrt{2} ) = 3 \\ \\ {x}^{3} = (2 \sqrt{2} ) \\ \\ x = \sqrt[3]{(2 \sqrt{2}) } \\ \\ x = \sqrt[3]{ (\sqrt[2]{8} )} \\ \\ x = \sqrt[3]{(\sqrt[2]{ {2}^{3}) } } \\ \\ x = \sqrt[3]{ {2}^{ \frac{3}{2} } } \\ \\ x = {2}^{( \frac{3}{2} \div 3)} \\ \\ x = {2}^{ \frac{3}{2} \times \frac{1}{3} } \\ \\ x = {2}^{ \frac{1}{2} } \\ \\ x = \sqrt[2]{2} \\ \\ </p><p>$