Required knowledge points of mathematics in college entrance examination: logarithmic definition

If the x power of a is equal to n (a >; 0, and a is not equal to 1), then the number x is called the logarithm of n with a as the base, and is recorded as x=logaN. Where a is called the base of logarithm and n is called real number.

Note: 1. Logarithm based on 10 is called ordinary logarithm and recorded as lg.

2. Logarithm with irrational number E as the base (e=2.7 1828 ...) is called natural logarithm, and it is recorded as ln.

3. Zero has no logarithm.

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

Logarithmic formula: a compulsory knowledge point of mathematics in college entrance examination

Required knowledge points of mathematics in college entrance examination: the definition of logarithmic function

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, +∞). 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.

Required knowledge points of mathematics in college entrance examination: the nature of logarithmic function

Solution of domain: the domain of logarithmic function y=logax is {xè x >; 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 always passes through the fixed point (1, 0).

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

That is, if y=logab (where a >；; 0，a≠ 1，b & gt0)

When a> 1, b> is at 1, y = logab & gt0;

When 0

When a> 1, 0 <; B< at 1, y = logab.