Question

Solve for x
8*2^(2x)+4*2^(x+1)=1+2^x

Answer 1

$8*2^{2x}+4*2^x*2^1=1+2^x\\\\Let\ 2^x=y,\ \ x=Log_2\ y\\\\8y^2+4*2y=1+y\\\\8y^2+7y-1=0\\\\8y^2+8y-y-1=0\\\\8y(y+1)-(y+1)=0\\\\(8y-1)(y+1)=0\\\\y=-1\ \ or\ \ 1/8\\\\y\ cannot\ be\ negative,\ as\ y=2^x\\\\y=\frac{1}{2^3}\\\\x=Log_2\ y=-Log_2\ 2^3=-3$

Answer 2

To solve this question, you need to know logarithms.
Taking log with base 2 on both sides, we get
log8 + 2xlog2 + log4 + (x+1)log2 = log1 + xlog2
3 + 2x + 2 + x + 1 = x
-2x = 6
x = -3