论文部分内容阅读
问题:比较log_67与log_78的大小. 思考:此问题用求差法、求商法.找中间值法.直接转化为指数形式等常用的比较两数的方法均不能奏效.通过查对数表可得到log_67≈1.086,log_78≈1.069,显然log_67>log_78.但对于一般地比较log(n 1)n与log_n(n+1),(n∈N,且n≠1)的问题又将如何解决呢?若用求导数的方法来判断函数y=log_n(n+1)(n∈N,n≠1)的单调性,这也不是一个容易解决的问题. 此问题中,log_67与log_78都在区间(1,2)内,差异微小(小于0.02),因之不易区别其大小.设想,如果把它们相同的整数部分“1”舍弃,只比较其小数部分.这如同用显微镜看物体,把细微处放大后,就容易发现其异同.故称此法为显微法.
Question: Compare the size of log_67 with log_78. Thinking: This problem uses the difference method, the quotient method. Find the intermediate value method. Directly converted to the index form and other commonly used methods to compare two numbers can not work. By checking the logarithm table can be obtained Log_67≈1.086, log_78≈1.069, obviously log_67>log_78. But for the general comparison of log(n 1)n and log_n(n+1), (n∈N, and n≠1), how will the problem be solved? If we use the derivative method to determine the monotonicity of the function y=log_n(n+1)(n∈N,n≠1), this is not an easy problem to solve. In this problem, both log_67 and log_78 are in the interval ( In 1,2), the difference is small (less than 0.02), so it is not easy to distinguish the size. It is assumed that if the same integer part “1” is discarded, only the fractional part is compared. This is like looking at the object with a microscope and putting the details After amplification, it is easy to find the similarities and differences. Therefore, this method is called microscopy.