Question

Solve: $2^{2x+3}-9\times 2^x+1=0$

Answer 1

$2^{2x}\times 2^3-9\times 2^x+1=0$
$\Rightarrow 8y^2-9y+1=0$ [Taking $2^x=y$]
$\Rightarrow 8y^2-8y-y+1=0$
$\Rightarrow (8y-1)(y-1)=0\Rightarrow y=\frac{1}{8}Or1$
When $y=\frac{1}{8}\Rightarrow 2^x=2^{-3}\Rightarrow x=-3$
When $y=1\Rightarrow 2^x=2^0\Rightarrow x=0$