Inequação exponencial

Inequação

O valor de x na inequação (2/3)^(2+x)≥ (9/4)^(3x-1) ,pode ser:

a)0

b)1                                                        

c)2

d)3

e)-0,5

Resposta:

2/3)^(2+x) ≥(9/4)^(3x-1),mas (9/4) = (3/2)²

(2/3)^(2+x) ≥ (3/2)^(3x-1),mas (3/2) = (2/3)-¹
(2/3)^(2+x)≥[(2/3)-¹]^(3x-1)
(2/3)^(2+x)≥(2/3)^[-1.(3x-1)]
(2/3)^(2+x)≥(2/3)^(-3x+1)
2 -1≥-3x-x
1 ≥ -4x
-1≤ 4x
x ≤ -1/4
x ≤ - 0,25
letra e).