Question

qual a solucao da equacao exponencial nos numeros reais ?
$\sqrt{81} ^{6x-2} = \sqrt[3]{243} ^{4x-2}$

Answer 1

$(\sqrt{3^4})^{6x-2}=(\sqrt[3]{3^5})^{4x-2}\\\\(3)^{\frac{4}{2}\cdot(6x-2)}=(3)^{\frac{5}{3}\cdot(4x-2)}\\\\12x-4=\frac{20x}{3}-\frac{10}{3}\\\\36x-12=20x-10\\\\16x=2\\\\x=\frac{1}{8}\\\\\boxed{x=2^{-3}}$