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比较几个数大小的习题,题型虽小,但解法却很灵活,一般都不易由观察直接得解,故需根据题意寻找适当的间接方法,本文介绍几种,供读者参考。一选取媒介值比较例1 试比较0.3~2、lg0.3、2~(0.3)三数的大小。解取媒介值0、1。∵0<0.3~2<1,lg0.3<0,2~(0.3)>1, ∴lg0.3<0.3~2<2~(0.3) 例2 试比较log_23与log_34的大小。解∵log_23=log_29~(1/2)>log_28~(1/2)=3/2, log_34=log_316~(1/2)log_34 媒介值选取的原则是:①能直接与已知数中任何一数比较大小;②媒介值应介于所比较的二
Comparing several numbers and sizes of exercises, the type of questions is small, but the solution is very flexible. Generally, it is not easy to obtain solutions from observation. Therefore, it is necessary to find appropriate indirect methods according to the questions. This article introduces several types for readers’ reference. A medium value comparison example 1 is selected to compare the size of three numbers of 0.3~2, lg0.3, and 2~(0.3). Detach media values 0, 1. ∵ 0<0.3~2<1, lg0.3<0, 2~(0.3)>1, ∴lg0.3<0.3~2<2~(0.3) Example 2 Compare the sizes of log_23 and log_34. Solution log_23=log_29~(1/2)>log_28~(1/2)=3/2, log_34=log_316~(1/2)log_34 The principle of the media value selection is: 1 can directly compare with any number of known numbers; 2 media values should be between the two compared