Question

raiz 5 de 2^x* raiz 3 de 4^x = raiz 2 de 8^-x

Answer 1

$\sqrt[5]{ 2^{x} } . \sqrt[3]{ 4^{x} } = \sqrt{ 8^{-x} }$

$2^{ \frac{x}{5} } . 4^{ \frac{x}{3} } = 8^{ \frac{-x}{2} }$

$2^{ \frac{x}{5} } . ( 2^{2} )^{ \frac{x}{3} } = ( 2^{3} )^{ \frac{-x}{2} }$

$2^{ \frac{x}{5} } . 2 ^{ \frac{2x}{3} } = 2^{ \frac{-3x}{2} }$

$2 ^{ \frac{x}{5}+\frac{2x}{3} } = 2^{ \frac{-3x}{2} }$

$2 ^{ \frac{3x}{15}+\frac{10x}{15} } = 2^{ \frac{-3x}{2} }$

$2 ^{ \frac{13x}{15} } = 2^{ \frac{-3x}{2} }$

$\frac{13x}{15}=\frac{-3x}{2}$

$\frac{13x}{15}+\frac{3x}{2}=0$

$\frac{26x}{30}+\frac{45x}{30}=0$

$\frac{71x}{30}=0$

$x=0$