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Question Number 136256 by EDWIN88 last updated on 20/Mar/21
log(x−2)(10−3x)<2
Answered by liberty last updated on 20/Mar/21
(1)10−3x>0;3x−10<0 x<103 (2)log(x−2)(10−3x)<log(x−2)(x−2)2 (x−2−1)(10−3x−(x−2)2)<0 ⇔(x−3)(10−3x−x2+4x−4)<0 (x−3)(−x2+x+6)<0 ⇔(x−3)(x2−x−6)>0 (x−3)(x−3)(x+2)>0 (x−3)2(x+2)>0 ⇒−2<x<3∪x>3 (3)x−2>0,x>2 Thesolutionsetis(2,3)∪(3,103)
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