Logarithm based on e is usually used for ln, and e is also a transcendental number. E is widely used in science and technology, and the logarithm with the base of 10 is generally not used.
brief introduction
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 base, and it is denoted as x=loga N, where a is called the base of logarithm and n is called a real number.
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, scaled by a constant factor. This leads to a logarithmic spiral.
Benford's law about the distribution of pre-derivatives can also be explained by scale invariance. Logarithm is also related to self-similarity. For example, the logarithmic algorithm appears in the algorithm analysis, and the algorithm is decomposed into two similar smaller problems, and their solutions are patched, and the problem is solved.