2、log(a)(a)= 1

3、log(a)(MN)= log(a)(M)+log(a)(N)；

4、log(a)(M÷N)= log(a)(M)-log(a)(N)；

5、log(a)(M^n)=nlog(a)(M)

6、log(a)[m^( 1/n)]=log(a)(m)/n

Extended data:

Generally speaking, logarithmic function is a function with power (true number) as independent variable, exponent as dependent variable and base as constant.

Logarithmic function is one of the six basic elementary functions. Where the logarithm is defined as:

If ax = N(a>；; 0, and a≠ 1), then the number x is called the logarithm of the base of n, denoted as x=logaN, and read as the logarithm of the base of n, where a is called the base of logarithm and n is called a real number.

In general, the function y = logax(a >；; 0, and a≠ 1) is called logarithmic function, that is, a function with power (real number) as independent variable, exponent as dependent variable and base constant as constant is called logarithmic function.

Where x is the independent variable and the domain of the function is (0, +∞), that is, x >；; 0。 It is actually the inverse function of exponential function, which can be expressed as x=ay. Therefore, the stipulation of a in exponential function is also applicable to logarithmic function.

Rational and irrational index

If it is a positive integer, it means that the addition and subtraction of the factor is equal to:

But if it is a positive real number not equal to 1, this definition can be extended to any real number in a field (see power). Similarly, the logarithmic function can be defined as any positive real number. For every positive base not equal to 1, there is a logarithmic function and an exponential function, which are reciprocal functions.

Logarithm can simplify multiplication to addition, division to subtraction, power operation to multiplication and root operation to division. Therefore, before the invention of electronic computers, logarithmic pairs were very useful for lengthy numerical operations and were widely used in astronomy, engineering, navigation, surveying and mapping and other fields. They have important mathematical properties and are still widely used today.

Complex logarithm

Complex logarithm calculation formula

The natural logarithm of a complex number, the real part is equal to the natural logarithm of the module of the complex number and the imaginary part is equal to the radiation angle of the complex number.