解不等式：log1/2(x2−x−2)＞log1/2(x−1)−1．
问题描述：
解不等式：log
(x2−x−2)＞log1 2
(x−1)−1． 1 2
答
原不等式变形为log
(x2−x−2)＞log1 2
(2x−2)．1 2
所以原不等式⇔
⇔
x2−x−2＞0 x−1＞0
x2−x−2＜2x−2
⇔
(x−2)(x+1)＞0 x−1＞0
x2−3x＜0
⇔2＜x＜3．
x＞2 0＜x＜3
故原不等式的解集为{x|2＜x＜3}．