Question

Resolver a equação exponencial

Answer 1

0,2=2/10=1/5=5⁻¹

$\sqrt{ {5}^{x} }. {25}^{x + 1} = ({ {5}^{ - 1}) }^{1 - x} \\ {5}^{ \frac{x}{2} } . { ({5}^{2}) }^{x + 1} = {5}^{x - 1} \\ {5}^{ \frac{x}{2} } . {5}^{2x + 2} = {5}^{x - 1}$

${5}^{ \frac{x}{2} + 2x + 2} = {5}^{x - 1} \\ {5}^{ \frac{x + 4x + 4}{2} } = {5}^{x - 1} \\ {5}^{ \frac{5x + 4}{2} } = {5}^{x - 1}$

$\frac{5x + 4}{2} = x - 1 \\ 5x + 4 = 2x - 2 \\ 5x - 2x = - 4 - 2 \\ 3x = - 6$

$x = - \frac{6}{ 3} = - 2$