No matter what the base of logarithm is, when N= 1, the value is equal to 0.
If the x power of a is equal to n (a >; 0, and a is not equal to 1), then the number x is called the logarithm of n with a as the base, and is recorded as x=logaN. Where a is called the base of logarithm and n is called real number.
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Logarithmic history
It was Napier's friend H.Briggs (1561-1631) who transformed the logarithm and made it widely spread. He found it inconvenient to use logarithm by studying the Handbook of Wonderful Logarithm Law, so he agreed with Napier to set logarithm as 1.
Because the number system used is decimal, it has advantages in numerical calculation. 1624, Briggs published logarithmic arithmetic, and published 1~20000 and 90000 ~ 10000 as the cardinal numbers.
According to the principle of logarithmic operation, people also invented the logarithmic slide rule. For more than 300 years, the logarithmic slide rule has been an indispensable computing tool for scientists, especially engineers and technicians. It was not until the 1970s that it gave way to electronic calculators. Although the logarithmic slide rule and logarithmic table are no longer important as a calculation tool, the logarithmic thinking method still has vitality.
From the process of logarithmic invention, we can find that Napier did not use the reciprocal relationship between exponent and logarithm when discussing the concept of logarithm. The main reason for this situation is that there was no clear concept of exponent at that time, and even the exponent symbol was written by French mathematician Descartes (R.Descartes, 1596- 1650) more than 20 years later.
It was not until the18th century that the Swiss mathematician Euler discovered the reciprocal relationship between exponent and logarithm. In a book published by 1770, Euler was first used to define it. He pointed out: "Logarithm originates from exponent". The invention of logarithm preceded exponent and became a rare story in the history of mathematics.
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