What is the function of lg?

Logarithmic function.

Lg logarithm is based on 10.

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:

What if ax? = N(a & gt； 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.

Extended data:

The domain of logarithmic function y=logax is {xèx >；; 0}, but when solving the domain of logarithmic compound function, we should not only pay attention to being greater than 0, but also pay attention to the fact that the base number is greater than 0 and not equal to 1. If the domain of function y=logx(2x- 1) is required, it must satisfy x >；; 0 and x≠ 1

And 2x-1>; 0, get x> 1/2 and x≠ 1, that is, its domain is {x丨 x >；; 1/2 and x≠ 1}

Range: real number set r, obviously the logarithmic function is unbounded;

Fixed point: the function image of logarithmic function always passes through the fixed point (1, 0);

Monotonicity: a> is at 1, which is a monotone increasing function on the definition domain;

When 0<a< 1, it is a monotonic decreasing function on the domain;

Parity: Non-odd non-even function

Periodicity: Not a periodic function.

Symmetry: none

Maximum value: None

Zero: x= 1

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: