Question

Calcular o valor de x na igualdade log9 3 raiz de 27=x

Answer 1

$Resolu\c{c}\~ao \to \left\{\begin{array}{ccc}log_{9}\ 3\sqrt{27} = x\\\\9^x = 3\sqrt{27}\\\\(3^2)^x = 3*\sqrt{3^3}\\\\3^{2x} = 3*3^{\frac{3}{2}}\\\\3^{2x} = 3^{1+\frac{3}{2}}\\\\3^{2x} = 3^{\frac{5}{2}}\\\\2x = \frac{5}{2}\\\\4x = 5\\\\\boxed{\boxed{x = \frac{5}{4}}}\end{array}\right$

Espero ter ajudado. =^.^=