比较两个数的大小有多种方法,如减法、比值法,或者利用已有基本初等函数的性质比较大小。但是在比较2014~(2015)与2015~(2014)两数的大小~([1]),用上述方法解决有一定的困难。本文主要讨论相关函数f(x)=a~x=x~a的性质。1函数f(x)=a~x-x~a(a≥3)的性质及应用首先,设函数f(x)=a~x-x~a,其中a∈Z_+。可得f′(x)=a~xln a-ax~(a-1),继续求导数,可得 There are many ways to compare the size of two numbers, such as subtraction, ratio method, or the size of the basic elementary functions. However, comparing the magnitude of (~ [1]) between the two numbers 2014 ~ (2015) and 2015 ~ (2014), some difficulties have been solved by the above method. This paper mainly discusses the properties of the correlation function f (x) = a ~ x = x ~ a. 1 The Function f (x) = a ~ x-x ~ a (a≥3) Properties and Applications First, let f (x) = a ~ x-x ~ a, where a∈Z_ +. Available f ’(x) = a ~ xln a-ax ~ (a-1), continue to find the derivative, available