In high school, we learned the definition of logarithms, the operation rules of logarithms, and the definition and properties of logarithmic functions. As a commonly used basic elementary function, let’s summarize it as follows.

　　1. Definition of logarithmic function

　　The inverse function of the exponential function is called the logarithmic function and is written as

( is a constant, and , ).

Its domain is .

　　When , the logarithmic function increases monotonically ;

　　When , the logarithmic function decreases monotonically (as shown in the figure).

[ Animation ]

        The logarithmic function with as the base is called the natural logarithmic function and is recorded as

.

The logarithmic function with base  called the common logarithmic function, written as

.

　　2. Mutual conversion of exponential expression and logarithmic expression: According to
　　the definition, when , and , there is

.

　　3. Logarithmic identity:

;

.

　　4. The influence of base on logarithmic function