Question

log2(2^x-1)log2(2^(x+2)-4=3

log2(2^x-1)log2(2^(x+2)-4）=3

Answer 1

设t=log2(2^x-1)
则log2(2^(x+2)-4）=2+t
原式=t*（2+t）=3
t=-3ort=1
log2(2^x-1)=-3
2^x-1=1/8
2^x=9/8
x=2log2(3)-3
log2(2^x-1)=1
2^x-1=2
2^x=3
x=log2(3)
综上
x=2log2(3)-3 or x=log2(3)

Answer 2

麻烦你把你方程的括号补齐。

Answer 3

log2(2^x-1)log2(2^(x+2)-4=3
令log2(2^(x-1))=y 则log2(2^(x+2))=log2(2^(x-1+3))=log2(2^(x-1))+log2(8)=y+3
原方程化为
y(y+3)-4=3
y²+3y-7=0
(y+3/2)²=37/4
y=-3/2+√37/2 y=-3/2-√37/2
那么
log2(2^(x-1))=-3/2+√37/2
2^(-3/2+√37/2)=2^(x-1)
x-1=-3/2+√37/2
x=-1/2+√37/2
同样，另一个解是 x=-1/2-√37/2