In mathematics, logarithm is the reciprocal 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.
Power multiplication allows any positive real number to be raised to any real power, and always produces positive results, so the logarithm can be calculated for any two positive real numbers b and x whose b is not equal to 1. 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.
Logarithmic function is a function with power (real number) as independent variable, exponent as dependent variable and base constant as constant. Logarithmic function is one of the six basic elementary functions. Definition of logarithm: if ax? = N(a & gt； 0, and a≠ 1), then the number x is called the logarithm with the base of n, which is recorded as x=logaN and read as the logarithm with the base of n.
A is called the base of logarithm and n is called real number. In general, the function y = logax(a >；; 0, and a≠ 1) is called logarithmic function, that is, a function with power (real number) as independent variable, exponent as dependent variable and base constant as constant is called logarithmic function. Where x is the independent variable and the domain of the function is (0, +∞), that is, x >；; 0。
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.
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.