precalculus
posted by Mike .
3(4^x)2^(x+2) = 1

3(4^x)2^(x+2) = 1
3(2^2)^x  (2^x)(2^2) + 1 = 0
3(2^x)^2  4(2^x) + 1 = 0
let 2^x = m
3n^2  4m + 1 = 0
(3m  1)(m  1) = 0
m = 1/3 or m = 1
so 2^x = 1/3
x = ln(1/3)/ln2 = appr. 1.585
or
2^x = 1
x = 0