Logarithmic function is a function with power (real number) as independent variable, exponent as dependent variable and base constant as constant. Logarithmic function is one of the six basic elementary functions. Definition of logarithm: if ax = n(a >；; 0, and a≠ 1), then the number x is called the logarithm with the base of n, which is recorded as x=logaN and read as the logarithm with the base of n.

Where a is called the base of logarithm and n is called 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. "log" is the abbreviation of Latin logarithm, which is pronounced as [English ][l? π] [America ][l? ɡ,lɑɡ]。

Rational and irrational index

If it is a positive integer, it means that the addition and subtraction of the factor is equal to: However, if it is a positive real number that is not equal to 1, this definition can be extended to any real number in a domain (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.

Note: Negative numbers and 0 have no logarithm. Two classic words:

The bottom true logarithm is positive and the bottom true logarithm is negative. The explanation is as follows: that is, if y=logab (where a >；; 0, a≠ 1, b>0) when 0