Question

Estou com uma dúvida na seguinte equação exponencial: (1/3)^-x+2 =√9 elevado a quarta

Answer 1

(1/3)^(-x+2) = 9^(1/4),
(1/3)^(-x+2) = (3)^2*(1/4),
(1/3)^(-x+2) =3^(1/2),
(1/3)^(-x+2) = (1/3)^[(-1)(1/2)];
(1/3)^(-x+2) = (1/3)^(-1/2);

Portanto, -x+2 = 1/2;
x = 2 + 1/2,
x = 5/2.

Answer 2

$( \frac{1}{3})^{-x+2}= \sqrt[2]{9^4} \\ \\ (3^{-1})^{-x+2}=9^{ \frac{4}{2}} \\ \\ 3^{x-2}=9^2 \\ \\ 3^{x-2}=(3^2)^2 \\ \\ 3^{x-2}=3^4 \\ \\ x-2=4 \\ \\ x=2+4 \\ \\ x=6$


S={6}