If a n = b (a > 0, and a≠ 1), the number n is called the logarithm of b with a base, and it is called n = log (a) b, where a is a subscript, a is called "base" and b is called "true 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.

Extended data:

Logarithm has many applications both inside and outside mathematics. Some of these events are related to the concept of scale invariance. For example, each chamber of the Nautilus shell is a rough copy of the next chamber, scaled by a constant factor. This leads to a logarithmic spiral. Benford's law about the distribution of pre-derivatives can also be explained by scale invariance. Logarithm is also related to self-similarity.

For example, the logarithmic algorithm appears in the algorithm analysis, and the algorithm is decomposed into two similar smaller problems, and their solutions are patched, and the problem is solved. The size of self-similar geometric shapes, that is, shapes whose parts are similar to the whole image, is also based on logarithm.

Arithmetic of logarithm:

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