Question

$2 ^{x+1} +4 ^{x} leq 80$

Answer 1

$2^{x+1}+4^x leq 80 \ 2^xcdot2+4^x leq 80$

Замена:
$2^x=t \ \ 2t+t^2 leq 80 \ t^2+2t-80 leq 0 \ \t^2+2t-80= 0 \ t_1+t_2=-2 cup t_1t_2=80 \ t_1=-10 cup t_2=8 \ \ a textgreater 0 Rightarrow t in [-10;8]$

Обратная замена:
$2^x geq -10 \ 2^x leq 8 \ \ x in R \ 2^x leq 2^3 \ \ x in R \ x leq 3$

Ответ: $x in (- infty; 3]$