1、log(a) (M N)=log(a) M+log(a) N

2、log(a) (M÷N)=log(a) M-log(a) N

Log (m n = nlog (a)

4、log(a)b*log(b)a= 1

log(a) b=log (c) b÷log (c) a

Algorithm of exponent:

1, [a m] × [a n] = a (m+n) is the same as the base power, the base number is constant, and the exponents are added.

2.[a m]⊙[a n]= a(m-n) Divide by the power with the same base, and subtract the exponent with the same base.

3. [a m] n = the power of a (Mn), the cardinality is unchanged, exponential multiplication?

4. The power of the product of [ab] m = (a m) × (a m) is equal to the power of each factor, and then multiplied by the obtained power.

Extended data:

History of Logarithm:

At the turn of 16 and 17 century, with the development of astronomy, navigation, engineering, trade and military, it is urgent to improve the digital calculation method. In order to simplify the calculation in astronomy, John Napier (J.Napier,1550-1617) invented logarithm. The invention of logarithm is an important event in the history of mathematics, and the astronomical community is almost ecstatic about this invention.

Engels once called the invention of logarithm, the establishment of analytic geometry and the establishment of calculus1the three major achievements of mathematics in the 7th century. Galileo also said, "Give me space, time and logarithm, and I can create a universe."

Before the invention of logarithm, people were familiar with the method of converting the product of trigonometric functions into the sum or difference of trigonometric functions. German mathematician M.Stifel (about 1487- 1567) expounded the following correspondence in Comprehensive Arithmetic (1544):

At the same time, the operational nature of this relationship (that is, the multiplication, division, power and root of the upper row number correspond to the addition, subtraction, multiplication and division of the lower row number) has also been widely known. After years of research on the operation system, Napier published the Explanation of the Wonderful Logarithm Law in 16 14, in which the logarithmic method was expounded in geometric terms with the help of kinematics.

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