S.4 Maths. logarithmic question

((2^(2X+2)))+((2^(X+2)))=3
2^2x*2^2 + 2^x*2^2 = 3
4*2^2x + 4*2^x = 3
4(2^x)^2 + 4(2^x) - 3 = 0
[2(2^x) -1][2(2^x)+3] = 0
2^x = 1/2 or -3/2 (rejected, since 2^x > 0 for all real x)
2^x = 2^(-1)
x = -1

2x+2log2 + x+2log2=3
(2x+2+x+2)log2=3
3x+4log2=log1000
3x+4=log1000/log2
x=((log1000/log2)-4)/3

x = -1.

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