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通常情况下,比较大小的题目可以先计算出结果后再进行比较。不方便计算的,可以通过做商,看结果是否大于1。而有的题,用上述方法无法解答。例如小学生竞赛题:比较2013~(2014)和2014~(2013)的大小。我们可以用推理的方法解答。这两个幂是底数和指数互换形成的。底数和指数差1。先计算符合这种情形的数目比较小的幂值,根据结果推断后面数值的大小。其过程为:1~2<2~1,2~3<3~2,3~4>4~3,4~5>5~4,5~6>6~5,……除了前两个式子外,后面的式子均显示指数大的幂值大。由此我们推断出2013~(2014)>2014~(2013)。
Under normal circumstances, the size of the problem can be calculated after the results before comparing. Inconvenient to calculate, you can do business to see if the result is greater than 1. And some questions, with the above method can not answer. For example, the pupils’ contest questions: compare the sizes of 2013 ~ (2014) and 2014 ~ (2013). We can use reasoning methods to answer. These two powers are formed by the exchange of base numbers and indices. Difference between base and index. First calculate the number of coincidences with this situation is relatively small exponential, according to the results of inferring the value of the size of the back. The process is as follows: 1 ~ 2 <2 ~ 1,2 ~ 3 <3 ~ 2,3 ~ 4> 4 ~ 3,4 ~ 5> 5 ~ 4,5 ~ 6> 6 ~ In the formula, the latter formulas show a large exponential value. From this we infer that 2013 ~ (2014)> 2014 ~ (2013).