解2log2^(x-5)=log2^(x-1)+1

题目

解2log2^(x-5)=log2^(x-1)+1

答案

2log2^(x-5)=log2^(x-1)+1
log2^(x-5)^2=log2^[2*(x-1)]
(x-5)^2=2(x-1)
x^2-12x+27=0
(x-3)(x-9)=0
x=3,x=9
代入检验
x=3使得log2^(x-5)无意义
所以x=9