In mathematics, logarithm is the inverse of power, just as division is the reciprocal of multiplication, and vice versa. This means that the logarithm of a number is an exponent that must produce another fixed number (radix). In a simple example, the logarithmic count factor in the multiplier. More generally, the power operation allows any positive real number to be raised to any power, and always produces positive results, so the logarithm of any two positive real numbers b and x whose b is not equal to 1 can be calculated.

If 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 x=logaN. Where a is called the base of logarithm and n is called real number.

Relationship between logarithmic function and exponent

Logarithmic function and exponential function with the same base number are reciprocal functions.

When a>0 and a≠ 1, ax=N, x=㏒aN.

On the symmetry of y = x.

The general form of logarithmic function is y=㏒ax, which is actually the inverse function of exponential function (two functions symmetrical about a straight line y=x are inverse functions), and can be expressed as x=ay. Therefore, the adjustment of a in exponential function (a >；; 0 and a≠ 1), and the graph on the right shows the function curves of a with different sizes: about the axis symmetry of X, when a >; At 1, the larger a is, the closer the image is to the X axis, when 0

It can be seen that the graphs of logarithmic functions are only symmetric graphs of exponential functions about the straight line y=x, because they are reciprocal functions.

The above contents refer to Baidu Encyclopedia-Logarithmic Function; Baidu Encyclopedia-Journal