Question

Solve the following equations
$2^{2x}-2^{x+3}+2^4=0$

Answer 1

$2^{2x}-2^{x+3}+2^4=0$

$\Rightarrow (2^x{)}^2-(2^x)2^3+16=0$

$\Rightarrow (2^x{)}^2-8(2^x)+16=0$

Let $2^x=y$

$\therefore y^2-8y+16=0$

$\Rightarrow (y-4{)}^2=0$

$\Rightarrow y=4$

$\therefore 2^x=4$

$\Rightarrow 2^x=2^2$

$\Rightarrow x=2$