What are the applications of exponential function and logarithmic function in life?

There are many practical problems related to exponential function and logarithmic function, such as social hot issues such as population growth and environmental protection, economic and life problems such as gross national product growth, cost increase and decrease, average growth rate, radioactive material transformation, temperature and other physical issues.

Exponential function y=ax (a > 0 and a≠ 1), logarithmic function y=logax (a > 0 and a≠ 1), exponential function y=ax and logarithmic function y=logax are reciprocal functions.

Extended data

Y=2x and x=logay are actually two different expressions of the corresponding relationship between X and Y, which are essentially the same. For example, when x=2, you can get y=4 no matter which expression you use. But the status of x and y has changed. Y is an exponential function of X, and X is a logarithmic function of Y. ..

According to the custom, if we use X as the independent variable of the function and Y as the dependent variable, then the inverse function y=2x(x∈R) x=logay(y∈(0, +∞)) of the exponential function becomes y=logax(x∈(0, +∞)). Therefore, to find the inverse function of y=2x, we can switch x and y to get x=2y, and then solve y=log2x.

Generally, the inverse function of the function y=f(x) is expressed as y=f- 1(x).

Therefore, when finding the inverse function of the function y=f(x) in the future, you can do this:

Step 1, exchange x and y in y=f(x) to get x = f (y);

Step 2, get y from x=f(y).