The domain of 1 and 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}

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

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

4. Monotonicity: a> at 1 is a monotone increasing function in the definition domain;

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

6. Parity: non-odd and non-even functions

7. Periodicity: Not a periodic function.

Log function generation history

From the end of 16 to the beginning of 17, at that time, the development of natural sciences (especially astronomy) often encountered a large number of accurate and huge numerical calculations, so mathematicians invented logarithms in order to seek simplified calculation methods.

Two series in integer arithmetic written by German Steve (1487- 1567) with 1544. On the left is the geometric series (called the original number), and on the right is arithmetic progression (called the representative of the original number, or index, which means index in German).

If you want to find the product (quotient) of any two numbers on the left, you only need to find the sum (difference) of its representative (exponent) first, and then put this sum (difference) on a primitive number on the left, then this primitive number is the product (quotient) you want. Unfortunately, Steve did not explore further and did not introduce the concept of logarithm.