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解对数不等式是高中数学的重要内容之一,但学生在解答时常犯一些错误。为此,应引导学生注意以下问题。一、要考虑函数的定义域例1、解不等式log2x2-3x+1x2+1logx2+2x-5x2+1误解:∵底数x2+11∴2x2-3x+1x2+2x-5解之得x2或x3∴原不等式的解集为(-∞,2)∪(3,+∞)分析:上述解答
Solving logarithmic inequality is an important part of high school mathematics, but students often make some mistakes in their answers. To this end, students should be guided to note the following questions. First, to consider the function of the domain Example 1, solution inequality log2x2-3x + 1x2 + 1logx2 + 2x-5x2 + 1 misunderstanding: ∵ bottom x2 +11 ∴ 2x2-3x + 1x2 + 2x-5 solution of x2 or x3 得The solution set of the original inequality is (-∞, 2) ∪ (3, + ∞) Analysis: The above solution