Question

Resolva a seguinte logaritimo:
logx 81=4/3

Answer 1

$log_{x}(81) = \frac{4}{3} \\ \\ 81 = x { }^{ \frac{4}{3} } \\ \\ x ^{ \frac{4}{3} } = 81 \\ \\ \sqrt[3]{x ^{4} } = 81 \\ \\ x ^{4} = 81 ^{3} \\ \\ x = 27 \\ \\ x = + 27 \\ x = - 27$

Answer 2

$log_{x} 81 = \frac{4}{3}$

$x^{\frac{4}{3} } = 81$

$\sqrt[3]{x^{4} } = 81$

$x^{4} = 81^{3}$

$x = \sqrt[4]{81^{3} }$

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

$x = \sqrt[4]{3^{12} }$

$x = 3^{3}$

$x = 27$

Espero ter ajudado.

Bons estudos!