log2(x-1)<log4(2-x)+1
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log2 (x-1)<log4 (2-x)+1
log2 (x-1)<1/2log2 (2-x)+1
2log2 (x-1)<log2 (2-x)+2
log2 (x-1)^2<log2 (2-x)+log2 4
log2 (x-1)^2<log2 4(2-x)
由于y=log2 x是个增函数,故:
(x-1)^2<4(2-x),即x^2+2x-7<0,解得:-1-2√2<x<-1+2√2
而由题设有:x-1>0,2-x>0,即1<x<2
综上所述:1<x<-1+2√2
log2 (x-1)<1/2log2 (2-x)+1
2log2 (x-1)<log2 (2-x)+2
log2 (x-1)^2<log2 (2-x)+log2 4
log2 (x-1)^2<log2 4(2-x)
由于y=log2 x是个增函数,故:
(x-1)^2<4(2-x),即x^2+2x-7<0,解得:-1-2√2<x<-1+2√2
而由题设有:x-1>0,2-x>0,即1<x<2
综上所述:1<x<-1+2√2
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