From the end of 16 to the beginning of 17, at that time, the development of natural sciences (especially astronomy) often encountered a large number of accurate and huge numerical calculations, so mathematicians invented logarithms in order to seek simplified calculation methods.

German Steven (1487- 1567) used 1544 to write two series in integer arithmetic. On the left is the geometric series (called the original number), and on the right is the arithmetic series (called the representative of the original number, or index, which means index in German).

If you want to find the product (quotient) of any two numbers on the left, you only need to find the sum (difference) of its representative (exponent) first, and then put this sum (difference) on a primitive number on the left, then this primitive number is the product (quotient) you want. Unfortunately, Steve did not explore further and did not introduce the concept of logarithm.

Napier is quite good at numerical calculation. The "Napier algorithm" he created simplifies the multiplication and division operation, and its principle is to replace multiplication and division with addition and subtraction. His motivation for inventing logarithm is to find a simple method to calculate spherics. He constructed the so-called logarithmic square method based on a very unique idea related to particle motion, whose core idea is the connection between arithmetic progression and geometric sequence. He expounded the principle of logarithm in Description of Wonderful Logarithm Table, which was later called Napier Logarithm and named Nappe. ㏒ X。 Its relationship with natural logarithm is as follows

Take a nap. ㏒x= 107㏑( 107/x)

Therefore, Napier logarithm is neither a natural logarithm nor an ordinary logarithm, which is far from today's logarithm.

The Swiss piccard (1552- 1632) also independently discovered logarithms, probably earlier than Napier, but published later (1620).

Briggs of Britain created the ordinary logarithm in 1624.

16 19, the new logarithm written by Peter in London makes the logarithm closer to the natural logarithm (based on e=2.7 1828 ...).

The invention of logarithm played an important role in the development of society at that time. As the scientist Galileo (1564- 1642) said, "Give me time, space and logarithm, and I can create a universe". Another example is18th century mathematician Laplace (1749- 1827), who also mentioned that "shortening the calculation time by logarithm can double the life span of astronomers".

Proportion and Logarithm, the first logarithmic work introduced to China, was edited by Polish Muniz (161-kloc-0/-656) and China Xue Fengzuo in the middle of17th century. At that time, in lg2=0.30 10, 2 was called "real number", 0.30 10 was called "pseudo number", and the real number and pseudo sequence were in one table, so it was called logarithmic table. Later, it was changed from "pseudo number" to "logarithm".

Dai Xu (1805- 1860), a mathematician in the Qing Dynasty, developed a variety of quick methods for finding logarithm, including logarithmic simplification (1845) and continuous logarithmic simplification (1846). 1854, the British mathematician Yue Se (1825- 1905) was very impressed when he saw these works.

Nowadays, middle school mathematics textbooks all talk about "exponent" first, and then introduce the concept of "logarithm" in the form of inverse function. But in history, on the contrary, the concept of logarithm did not come from index, because there was no clear concept of fractional index and irrational index at that time. Briggs once suggested to Napier that logarithm should be expressed by power exponent. 1742, J. William (1675- 1749) wrote the preface of G. William's logarithm table, in which the exponent can define logarithm. Euler clearly pointed out in his famous book On Infinitesimal Analysis (1748) that logarithmic function is the inverse function of exponential function, which is consistent with the current textbooks.