Question

Alguém sabe resolver essa equação (1/3) elevado a -x+2= a raiz quarta de nove

Answer 1

Olá,

(1/3)^(-x+2) = (1/3)^(2-x) = (1/3)^2 / (1/3)^x
(9)^1/4 = (3^2)^1/4 = (3)^(2×1/4) = (3)^(1/2) = (1/3)^(-1/2)

(1/3)^2 / (1/3)^x = (1/3)^(-1/2)
(1/3)^2 = (1/3)^(-1/2) · (1/3)^x

2 = -1/2+x
x = 2+1/2
x = (4+1)/2
x = 5/2

Answer 2

(1/3) elevado a -x+2= a raiz quarta de nove
(1/3)^-x + 2 = 9^1/4

(3^-1)^-x + 2 = (3^2)^1/4

3^x - 2 = 3^2/4

x - 2 = 2/4

4x - 8 = 2 ==> 4x = 8 + 2

4x = 10 ==> x = 10/4  ou x = 5/2