2^x-2^(-x+3)=2,求x

2^x-2^(-x+3)=2


x-(-x+3)=1{因為2^x-2^(-x+3)=2^1所以刪掉底數2,可得x-(-x+3)=1}

x+x-3=1

2x=4

∴x=2

2^x - 2^(-x + 3) = 2
2^x - 82^(-x) - 2 = 0
Let 2^x = y
so y - 8/y - 2 =0
y^2 - 2y - 8 = 0
(y - 4)(y +2) = 0
y = 4 and - 2
that is
2^x = 4 = 2^2, so x = 2.
2^x = - 2 (rej.).