1, in a simple case, the logarithmic counting 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.

2. Logarithmic function Generally speaking, if the power of A (A is greater than 0, A is not equal to 1) is equal to N, then this number B is called the logarithm of N with A as the base, and it is recorded as log an=b, where A is called the base of logarithm and N is called a real number.

If the real number formula has no root number, then as long as the real number formula is greater than zero, if there is a root number, it is required that the real number is greater than zero and the radix in the root number formula is greater than zero and not 1. Why should the base of logarithmic function in an ordinary logarithmic formula be greater than 0 instead of 1? A

3. loga (1) = 0loga (a) =1,loga(MN)=logaM+logaN, loga (m/n) = logaM-logan, logaM (log (n) is equal to the n power of m in logam. (mn)=log(a)(m)+log(a)(n),log(a)(m÷n)=log(a)(m)-log(a)(n),log(a)(m^n)=nlog(a)(m),log(a^n)m= 1/nlog(a)(m).

Application of logarithmic logging:

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. The size of self-similar geometric shapes, that is, shapes whose parts are similar to the whole image, is also based on logarithm. Logarithmic scale is useful for quantifying the relative change of value relative to its absolute difference.

In addition, because the logarithmic function log(x) grows very slowly for larger x, the logarithmic scale is used to compress large-scale scientific data. Logarithm also appears in many scientific formulas, such as tsiolkovsky rocket equation, Fenske equation or Nernst equation.