Question

como calculo raíz 5 de 4 ^x=1/raiz de 8,  

Answer 1

$\sqrt[5]{4^{x}}=\dfrac{1}{\sqrt{8}}\\\\\\4^{(x/5)}=(\sqrt{8})^{-1}\\\\\\(2^{2})^{(x/5)}=(\sqrt[2]{2^{3}})^{-1}\\\\\\2^{(2x/5)}=[2^{(3/2)}]^{-1}\\\\\\2^{(2x/5)}=2^{(-3/2)}$

Bases iguais, iguale os expoentes:

$\dfrac{2x}{5}=-\dfrac{3}{2}\\\\\\x=-\dfrac{3\cdot5}{2\cdot2}\\\\\\\boxed{\boxed{x=-\dfrac{15}{4}}}$

Answer 2

$\sqrt[5]{4^x}=\frac{1}{\sqrt8} \\ \\ 4^{\frac{x}{5}}=\frac{1}{8^{\frac{1}{2}}}\\ \\ 2^{\frac{2x}{5}}=\frac{1}{2^{\frac{3}{2}}}\\ \\ 2^{\frac{2x}{5}}=2^{-\frac{3}{2}}\\ \\ \frac{2x}{5}=-\frac{3}{2}\\ \\ 4x=-15\\ \\ x=-\frac{15}{4}$