The natural logarithm is the logarithm with the constant e as the base, and it is denoted as lnn(n >；; 0)。 It is of great significance in physics, biology and other natural sciences, and is generally expressed as lnx. Logx is also commonly used in mathematics to represent natural logarithm. The meaning of constant e is the limit value that can be achieved by doubling the growth continuously in unit time. When the real number in the natural logarithm lnN is a continuous independent variable, it is called a logarithmic function and is denoted as y=lnx(x is the independent variable and y is the dependent variable).
Generally speaking, logarithmic function is a function with power (true number) as independent variable, exponent as dependent variable and base as constant. Logarithmic function is one of the six basic elementary functions. Definition of logarithm: if ax = n(a >；; 0, and a≠ 1), then the number x is called the logarithm of the base of n, denoted as x=logaN, and read as the logarithm of the base of n, where a is called the base of logarithm and n is called a 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。 It is actually the inverse function of exponential function, which can be expressed as x=ay. Therefore, the stipulation of a in exponential function is also applicable to logarithmic function.