Question

Resolva esta equaçao 2^2x +( 2^x+1)=80

Answer 1

$2^{2x}+2^{x+1}=80\\ \\ (2^x)^2+2.2^x-80=0\\ \\ \boxed{y=2^x}\\ \\ y^2+2y-80=0\\ \\ \Delta=2^2-4.1.(-80)=4+320=324\\ \\ y=\frac{-2 \pm\sqrt{324}}{2}=\frac{-2 \pm18}{2}\\ \\ y_1=-10\\ \\ y_2=8\\ \\ \boxed{2^x=8\rightarrowx=3}$