history
The concept of logarithm begins with 16 14. Six years later, John Napier and Jost Bürgi published their own logarithmic tables. At that time, through a large number of exponentiation operations on the base close to 1, the logarithm of the specified range and precision and the corresponding real number were found. At that time, there was no rational power.
William Jones (British mathematician) 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 0.9999999 is quite close to1/e.
In fact, there is no need to do high-power and difficult operations. It took John Napier 20 years to calculate the equivalent of a million times multiplication. Henry Briggs (mathematician) suggested that Napier use 10 as the base, but failed. He partially compiled the common logarithm table in 1624 by his own method.
1649, alphonse Antonio de Sarasa (English: alphonse Antonio de Sarasa) interpreted the area under the hyperbola as logarithm. About 1665, isaac newton popularized the binomial theorem, and he will
The infinite series of natural logarithm is obtained by expanding the integral item by item. The first description of "natural logarithm" was found in the book Logarithm Mathematics published by Nicholas Mercator in 1668. He also independently discovered the same series, namely the Mercator series of natural logarithm. Around 1730, Euler defined two inverse functions: exponential function and natural logarithm.
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 invention of the logarithmic tool, multiplication can be turned into addition, that is:
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 function value table of logarithmic function y=lnx based on e is called natural logarithm table. The natural logarithm table generally consists of two parts, one is the natural logarithm table of [1, 10], and the other is the natural logarithm value of every integer power of 10. For a positive number x, it can be expressed in decimal form: x=q× 10n, where q∈[ 1, 10], then look up the table to find out lnq and ln 10n respectively, and add these two parts to get the value of lnx.
For example, 1 find ln4.5, in 10, ln 1.8.
Solution: You can find it directly from the table.
ln4.5= 1.504 1，
ln 10=2.3026，
ln 1.8=0.5878。
Example 2 Find ln 450 and ln 0.045.
Solution: ∫450 = 4.5x 102,
0.045=4.5x 10-2，
∴ ln450= ln4.5+ ln 102，
= 1.504 1 + 4.6052 = 6. 1093
ln 0.045= ln4.5+ ln 10-2
= ln4.5-in 102= 1.504 1-4.6052=﹣3. 10 1 1.
Note: the natural logarithm table is similar to the ordinary logarithm table, but they have important differences. The natural logarithm table provides the first number and mantissa.
The range of such forms is generally limited to 1.0~9.99. The value of natural logarithm not given in the table can be obtained by adding or subtracting the natural logarithm of the power of 10 with the value in this table.
Baidu encyclopedia-natural logarithm
Baidu encyclopedia-natural logarithm table