log2(x-1)

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log2(x-1)log2(x-1)log2(x-1)log2(x-1)log2(x-1)2log2(x-1)log2(x-1)^2log2(x-1)^2由于y=log2x是个增函数,故:(x-1)^

log2(x-1)
log2(x-1)

log2(x-1)
log2 (x-1)log2 (x-1)<1/2log2 (2-x)+1
2log2 (x-1)log2 (x-1)^2log2 (x-1)^2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而由题设有:x-1>0,2-x>0,即1综上所述:1