Loga(b)=logc(b)/logc(a), where a, b and c are positive numbers and a and b are not equal to 1, and log represents the logarithm with the base of c.

exponential function

Exponential function is one of the important basic elementary functions. Generally speaking, the function of y = a x (a is constant and a >；; 0, a≠ 1) is called exponential function, and the definition domain of the function is R. Note that in the definition expression of exponential function, the coefficient before a x must be the number 1, and the independent variable X must be in the exponential position, and it cannot be other expressions of X, otherwise it is not an exponential function.

Mathematical explanation

Exponential function is an important function in mathematics. This function applied to the value e is written as exp(x). It can also be written as ex, where e is a mathematical constant and the base of natural logarithm, which is about equal to 2.7 1828 1828, also known as Euler number.

When a> is in 1, the negative value of exponential function to x is very flat, and the positive value to x rises rapidly. When x equals 0, y equals 1. When 0

As a function of the real variable x

The image is always on the right side of the X axis and increases from left to right. It never touches the X axis, although it can be infinitely close to the X axis, so the X axis is the horizontal asymptote of this image. Its inverse function is natural logarithm ln(x), which is defined on all positive numbers X.

Sometimes, especially in science, the term exponential function is usually used in the following form.

K is a function of R, where A is called "base" and is any positive real number not equal to 1. Firstly, this paper mainly studies the exponential function based on Euler number e.

The general form of exponential function is

(a>0 and ≠ 1)(x∈R). From the above discussion about power function, we can know that if X can take a whole set of real numbers as the domain, then we only need to make A >: 0, a≠ 1.