I. Logarithm
1. In mathematics, logarithm is the inverse of power, just as division is the inverse 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 speaking, exponentiation allows any positive real number to be raised to any power, which always produces positive results.
2. Therefore, 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 = loga &；; Nbspn. where a is called the base of logarithm and n is called real number.
3. Application: 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.
Second, odd function.
1, odd function means that for a domain, the function f(x) with symmetrical origin has f(-x)=-f(x) in any x in the domain, so the function f(x) is called odd function. 1727, Euler, a young Swiss mathematician, submitted a paper (in Latin) to St. Petersburg Academy of Sciences, which solved the "rebound trajectory problem".
2. The concept of parity function is put forward for the first time. Nature: the difference between the sum or subtraction of two odd function is odd function; The difference between the sum or subtraction of even function and odd function is parity function; The quotient obtained by multiplying or dividing two odd function is an even function.
3. The quotient of the product or division of an even function multiplied by a odd function is odd function; Properties of odd function: If f(x) is odd function and the maximum (or minimum) of f(x) is m, then the minimum (or maximum) of f(x) is-m.