Logarithm based on constant e. Write lnn (n >; 0)。 It is of great significance in physics, biology and other natural sciences. The general representation is lnx. Logx is also commonly used in mathematics to represent natural logarithm. Because the basic property of logarithmic function passes through the fixed point (1, 0), that is, when x= 1, y=0, so ln 1 equals 0.

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). Generally speaking, power multiplication allows any positive real number to be raised to any real power, which 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 is not equal to 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.

Extended data

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 the base of n. Where a is called the base of logarithm, n is called real number, and x is called "logarithm with base of n". In particular, we call the logarithm with the base of 10 as the common logarithm and record it as lg. Logarithm based on irrational number e is called natural logarithm, and it is recorded as ln.

Zero has no logarithm. In the range of real numbers, negative numbers have no logarithm. ? In the range of imaginary numbers, negative numbers are logarithms. Actually, when θ=(2k+ 1)π, k is an integer, there is e(2k+ 1)πi+ 1=0, so ln(- 1) = In this way, the natural logarithm of any negative number has periodic multivalues.

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