解2log2^(x-5)=log2^(x-1)+1

来源:学生作业帮助网 编辑:六六作业网 时间:2024/05/09 15:18:32
解2log2^(x-5)=log2^(x-1)+1解2log2^(x-5)=log2^(x-1)+1解2log2^(x-5)=log2^(x-1)+12log2^(x-5)=log2^(x-1)+1l

解2log2^(x-5)=log2^(x-1)+1
解2log2^(x-5)=log2^(x-1)+1

解2log2^(x-5)=log2^(x-1)+1
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

x=9

x-5>0,x-1>0得x>5
2log<2>(x-5)=log<2>(x-1)+1
log<2>(x-5)²=log<2>(x-1)+log<2>2
log<2>(x²-10x+25)=log<2>(2x-2)
x²-10x+25=2x-2
x²-12x+27=0
(x-3)(x-9)=0
x=9
原方程的解为x=9