log2[(x-14)(x-2)]=3+log2(6-x).求x?.

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/05/09 03:36:20

有题意得：x≠14,2,6
log2[(x-14)(x-2)]=3+log2(6-x)
=>log2[(x-14)(x-2)]-log2(6-x)=3
=>[(x-14)(x-2)]/(6-x)=2^3
=>(x^2-16x+28)/(6-x)=8
=>x^2-16x+28=48-8x
=>x^2-8x-20=0
=>x=10或x=2(舍去)

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