题目内容
已知函数f（x）=|log3x|，0＜x3＜x1＜x2且x2=9x3，则f(
)+f(
)=（ ）
| x1 |
| x2 |
| x1 |
| x3 |
分析：由0＜x3＜x1＜x2且x2=9x3，可得
＞1，
＜
=
•
＜1，从而可得f(
)=|log3
|=-log3
，f（
）=|log3
|=log3
，根据对数的运算性质，代入可求
| x1 |
| x3 |
| 1 |
| 9 |
| x1 |
| x2 |
| 1 |
| 9 |
| x1 |
| x3 |
| x1 |
| x2 |
| x1 |
| x2 |
| x1 |
| x2 |
| x1 |
| x3 |
| x1 |
| x3 |
| x1 |
| x3 |
解答：解：∵0＜x3＜x1＜x2且x2=9x3，
∴
＞1，
＜
=
•
＜1
∴f(
)=|log3
|=-log3
=log3
，f（
）=|log3
|=log3
则f(
)+f(
)=-log3
+log3
=log3(
•
)=log3
=log39=2
故选C
∴
| x1 |
| x3 |
| 1 |
| 9 |
| x1 |
| x2 |
| 1 |
| 9 |
| x1 |
| x3 |
∴f(
| x1 |
| x2 |
| x1 |
| x2 |
| x1 |
| x2 |
| x2 |
| x1 |
| x1 |
| x3 |
| x1 |
| x3 |
| x1 |
| x3 |
则f(
| x1 |
| x2 |
| x1 |
| x3 |
| x1 |
| x2 |
| x1 |
| x3 |
| x1 |
| x3 |
| x2 |
| x1 |
| x2 |
| x3 |
故选C
点评：本题主要考查了对数的基本运算性质的应用，解题的关键是根据所给的0＜x3＜x1＜x2判断出
＞1，
＜
=
•
＜1的范围
| x1 |
| x3 |
| 1 |
| 9 |
| x1 |
| x2 |
| 1 |
| 9 |
| x1 |
| x3 |
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