**Definition of Exponential Function**

The exponential function f with base a is denoted by , where , and *x* is any real number. The function value will be positive because a positive base raised to any power is positive. This means that the graph of the exponential function will be located in quadrants I and II.

For example, if the base is 2 and x = 4, the function value f(4) will equal 16. A corresponding point on the graph of would be (4, 16).

**Definition of Logarithmic Function**

For *x* >0, *a*>0 , and , we have

Since *x* > 0, the graph of the above function will be in quadrants I and IV.

**Comments on Logarithmic Functions**

- The exponential equation could be written in terms of a logarithmic equation as .
- The exponential equation can be written as the logarithmic equation .
- Since logarithms are nothing more than exponents, you can use the rules of exponents with logarithms.
- Logarithmic functions are the inverse of exponential functions. For example if (4, 16) is a point on the graph of an exponential function, then (16, 4) would be the corresponding point on the graph of the inverse logarithmic function.
- The two most common logarithms are called
**common**logarithms and**natural**logarithms. Common logarithms have a base of 10, and natural logarithms have a base of*e*.

If you are interested in reviewing any of the following topics, click
the appropriate item:

- The properties of logarithms along with examples and problems, click on Properties
- The graphs of logarithms, with examples and problems, click on Graphs of Logarithms
- Change of base with respect to logarithms with examples and problems, click on Change of base
- The three rules of logarithms, with examples and problems, click on Rules of Logarithms
- Solving exponential and logarithms equations with examples and problems, click on Solving Equations
- Solving word problems involving exponential and logarithms functions with examples and problems, click on Solving Word Problems
- The properties of logarithms along with examples and problems, click on Properties

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