Question

$2^{x+1} +2^{x-2}-3.2^{-x+1}=30/2^{x}$

Answer 1

$2^{x+1}+2^{x-2}-3.2^{-x+1}=\frac{30}{2^x} \\ \\ 2.2^x+\frac{2^x}{4}-3.\frac{2}{2^x}=\frac{30}{2^x} \\ \\ 2.2^x+\frac{2^x}{4}-\frac{6}{2^x}=\frac{30}{2^x} \\ \\ \boxed{y=2^x} \\ \\ 2y+\frac{y}{4}-\frac{6}{y}=\frac{30}{y} \\ \\ 8y^2+y^2-24=120 \\ \\ 9y=144 \\ \\ y=16 \\ \\ 2^x=12 \\ \\ 2^x=2^2 \\ \\ \boxed{\boxed{x=4}}$