We can explain how the natural logarithm is "natural" from its original source. People used to use multiplication, which was very troublesome. After the invention of logarithmic tools, multiplication can be turned into addition.
Of course, mathematicians later studied this number countless times and found that its magical characteristics appeared in the logarithmic table not by accident, but quite naturally or inevitably. Therefore, it is called natural logarithm base.
Extended data:
The concept of logarithm begins with 16 14. Six years later, John Napier and Jost burgui published their own logarithmic tables. At that time, through a large number of exponentiation operations on the base close to 1, the logarithmic sum of the specified range and precision and the corresponding real number were found. At that time, the concept of rational number power had not yet appeared.
William Jones published the concept of power exponent in 1742. According to later generations, yost burgui's base number 1.000 1 is quite close to the base number e of natural logarithm, while John Napier's base number 0.99999999 is quite close to1/e.
In fact, there is no need to do such a difficult operation as increasing power. John Napier spent 20 years calculating the equivalent of millions of multiplication operations. Henry Briggs suggested that Napier take 10 as the base, but failed. He partially completed the compilation of the common logarithm table in 1624 by his own method.