Question

已知log_0.45（x+2）＞log_0.45（1-x），則實數(shù)x的取值范圍是

(-2，-

1

2

)

．

Answer 1

分析：根據(jù)真數(shù)大于零和對數(shù)函數(shù)的單調(diào)性列出方程，再求解即可．

解答：解：由y=log_0.45x在定義域上是減函數(shù)和真數(shù)大于零得，

x+2＜1-x x+2＞0 1-x＞0

，解得-2＜x＜-

1

2

，
故答案為：(-2，-

1

2

)．

點評：本題主要考查了對數(shù)函數(shù)的單調(diào)性應(yīng)用，易錯點在易忘對數(shù)的真數(shù)大于零．