Question

$( \sqrt{5} )^{x-3}= \frac{1}{625}$
defina o conjunto solução da equação

Answer 1

$(\sqrt{5} )^{x-3}= \frac{1}{625} \\ \\(5^{ \frac{1}{2} })^{x-3}= \frac{1}{5^4} \\ \\ (\diagup\!\!\!5^{ \frac{x}{2}- \frac{x}{3} })=\diagup\!\!\!5^{-4} \\ \\ \frac{x}{2}- \frac{3}{2}=-4 \\ \\ \frac{x-3}{\diagup\!\!\!2} = \frac{-8}{\diagup\!\!\!2} \\ \\ x-3=-8 \\ x=-8+3 \\ \boxed{\boxed{x=-5}} \\ \\ \\ \boxed{ S.:\{-5\}}$