The general form of logarithmic function is y=logax, which is actually the inverse function of exponential function (the image of two functions is symmetrical about a straight line, y=x is the inverse function), and it can be expressed as x = a y, so there is a provision in exponential function-a >; 0 and a≠ 1, different function diagrams will be formed for different sizes of a: 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

Application of Logarithm:

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, which is scaled by a constant factor, which creates a logarithmic spiral. Benford's law about the distribution of pre-derivative can also be explained by scale invariance, and logarithm is also related to self-similarity.

Logarithmic algorithm appears in algorithm analysis, which is solved by decomposing the algorithm into two similar smaller problems and modifying their solutions. The size of the self-similar geometric shape, that is, the shape of the part similar to the whole image, is also based on logarithm, and logarithmic scale is useful to quantify the relative change of the value opposite to its absolute difference.