## Discussion

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### Logarithms and Logarithmic Functions

Remember that a logarithm is just an exponent.

Understand that the log function and the exponential function are inverses of each other.

Use this to solve problems.

Solve logarithmic equations

*with the same base*by equating the expressions whose logarithms have been equated.Solve logarithmic inequalities

*with the same base*by applying the same inequality to the expressions whose logarithms have been compared.In solving logarithmic equations or inequalities, always check for extraneous solutions -- values which result in taking the logarithm of a non-positive value in the original equation or inequality. Exclude such values from the solution set.

### Logarithms and Logarithmic Functions

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

- Intro 0:00
- What are Logarithms? 0:17
- Examples
- Logarithmic Functions 4:09
- Graph of the Logarithmic Function 4:52
- Properties 9:08
- Inverse Property 10:47
- Equations 11:44
- Example
- Inequalities 14:45
- Equations with Logarithms on Both Sides 17:00
- Example
- Inequalities with Logarithms on Both Sides 19:17
- Example
- Lecture Example 1 20:31
- Lecture Example 2 22:38
- Additional Example 3
- Additional Example 4

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