Question

(Ufbp) a soluçao da equação da 2^x+1 - 2^x-1 + 2^x-2= 14

Answer 1

Basta chamar 2^x de y

2^x = y

$2^{x+1}-2^{x-1}+2^{x-2} = 14 \\ 2^{x}.2 - 2^{x}.2^{-1}+2^{x}.2^{-2}=14 \\ y.2-y. \frac{1}{2} +y. \frac{1}{4} =14 \\ \frac{8y}{4}- \frac{2y}{4}+ \frac{y}{4}=14 \\ \frac{7y}{4}=14 \\ 7y=56 \\ y= 8 \\ \\ 2^{x} = 8 \\ 2^{x}=2^{3} \\ x = 3$