E is widely used in science and technology, and the logarithm with the base of 10 is generally not used. Taking e as the base can simplify many formulas, and it is the most "natural", so it is called "natural logarithm" We can show how the natural logarithm is "natural" from how it was originally produced. People used to do multiplication by multiplication, which was very troublesome. After the tool of logarithm was invented, multiplication can be turned into addition, that is, log(a * b) = loga+logb. However, the premise of this is that I need to have a logarithmic table, know what loga and logb are, and then sum them up to know how many logs this sum is equal to. Although it was troublesome to compile logarithmic tables, it was once and for all, so a great mathematician began to compile logarithmic tables. But he encountered a problem, that is, what is the best base of this logarithmic table? 10? Or two? In order to determine the cardinal number, he made the following considerations: 1. When the number is in the range of 0. 1- 1, all multipliers/multiplicands can be multiplied by the power of 10. This can be done by scientific notation. 2. Now we only consider making a logarithmic table of numbers between 0- 1, so it is natural to use a number between 0- 1 as the cardinal number. (If you use a number greater than 1 as the base, then the logarithm is negative and not good-looking; ) The base between 3.0 and 1 cannot be too small, for example, 0. 1 is too small, which will lead to the logarithm of many numbers being fractions; Moreover, "the logarithm of two very different numbers is very small." For example, when the base number is 0. 1 and the difference between the two numbers is 10 times, the logarithmic value is only 1. In other words, for numbers that are not much different between 0.5 and 0.55, if the base is 0. 1, the logarithmic table must be accurate. 4. In order to avoid this shortcoming, the cardinality must be close to 1, such as 0.99, or even better. Generally speaking, it is 1- 1/X, and the larger the x, the better. After choosing a large enough x (the larger x is, the more accurate the logarithmic table is, but the more complicated it is to calculate this logarithmic table), you can calculate (1- 1/x)1= p1,(1-kloc-0). Moreover, if X is large, then P 1, P2, P3 ... are all close together, and can basically cover the interval between 0. 1 and 1 uniformly. 5. Finally, he adjusted it again, taking (1- 1/X) x as the base, so that the logarithmic value of P 1 is 1/X, the logarithmic value of P2 is 2/ X, and ... px is 1, so as to avoid it. The minimum difference between these two values is1/x.6. Now make the logarithmic table more accurate, and then x will be bigger. Mathematicians have calculated it many times, 1000, 1000, 100000. Finally, he found that when x becomes larger, the cardinal number (1- 1/x) X approaches a value. This value is 1/e, the reciprocal of the natural logarithm base (although it was not named at that time). In fact, if our first step is not to convert all values into 0. 1- 1, but into 1- 10, then the final result of the same discussion is E-the great mathematician is the famous Euler, and the name E of natural logarithm comes from the name of Euler. Of course, mathematicians have done countless studies on this number and found that its various magical things appear in the logarithmic table not by accident, but quite naturally or inevitably. Therefore, it is called natural logarithm base.