Expert: Ahmed Salami - 6/5/2011

Question
If 8(4^x-2^x)=2^(x+1)

Answer
Hi Ade,
8(4^x - 2^x) = 2^(x+1)
8(4^x - 2^x) = 2(2^x)
4(4^x - 2^x) = 2^x
4(4^x) - 4(2^x) = 2(2^x)
4(4^x) - 6(2^x) = 0
2(4^x) - 3(2^x) = 0
2(2^x)^2 - 3(2^x) = 0
(2^x)[2(2^x) - 3] = 0
Therefore,
2(2^x) - 3 = 0
2^x = 3/2
Taking logarithms,
log (2^x) = log (3/2)
x . log2 = log (3/2)
x = [log(3/2) / log2]

Regards