Generally speaking, if the power of B of a(a is greater than 0, and A is not equal to 1) is equal to N, then the number B is called the logarithm of N with the base of A, which is recorded as log aN=b and read as the logarithm of N with the base of A, where A is called the base of logarithm and N is called a real number. The general function y=log(a)X, (where a is a constant and n is called a real number. 0 and a is not equal to 1) is called logarithmic function, which is actually the inverse function of exponential function and can be expressed as x = a Y, so the stipulation of a in exponential function is also applicable to logarithmic function.

For example:

Logarithmic function is the inverse of power function. Y = 2 x is a power function. The inverse function of y = 2 x is x=log2y.

Definition of logarithm

If, that is, the x power of a is equal to n (a >; 0, and a≠ 1), then the number x is called the logarithm of n with a as the base, and is recorded as. Where a is called the base of logarithm, n is called real number, and x is called "logarithm with base of n".

1. In particular, we call the logarithm with the base of 10 the common logarithm and record it as lg.

2. Logarithm based on irrational number e (e=2.7 1828 ...) is called natural logarithm, and is recorded as ln.

3. Zero has no logarithm.

4. In the range of real numbers, negative numbers have no logarithm. [3]? In the range of complex numbers, negative numbers are logarithms.

Actually, if there is e(2k+ 1)πi+ 1=0, then ln(- 1) = (2k+1) π i has many periodic values, so that any negative number. For example: ln(-5)=(2k+ 1)πi+ln 5.