# Ch 10: Logarithms & Exponential Equations: College Math Lesson Plans

### About This Chapter

## Weekly Syllabus

Below is a sample breakdown of the Logarithms and Exponential Equations: College Math chapter into a 5-day school week. Based on the pace of your course, you may need to adapt the lesson plan to fit your needs.

Day | Topics | Key Terms and Concepts Covered |
---|---|---|

Monday | Exponential functions, growth and decay | Graphs of exponential functions, standard exponential function, asymptote and determination of starting value |

Tuesday | Evaluation of logarithms | Logarithmic form, natural base, natural log and change of base formula |

Wednesday | Logarithmic properties | Product, quotient and power properties; expanding, condensing and evaluating logs |

Thursday | Use of logarithms to solve exponential equations | Natural log and change of base formula |

Friday | Use of exponentials to solve logarithmic equations | Magnitude, product property and exponentiating |

### 1. What Is an Exponential Function?

Brand new technologies don't always catch on right away because they can be expensive and don't always work as well as they should. But once the price comes down, and they start to work better, it doesn't take very long before it seems like everyone has one. Learn about the numbers behind this, exponential functions!

### 2. Exponential Growth vs. Decay

How is it that it only takes four years for our computer to go from top-of-the-line to almost worthless? Well, it has something to do with what's called exponential decay, which we'll learn about here!

### 3. What is a Logarithm?

Logarithms can help you solve exponential functions. In this lesson, you will learn about how to work with and recognize logarithms, and how to use logarithm notation with an example problem about earthquakes!

### 4. How to Evaluate Logarithms

Using this lesson, you can get practice evaluating logarithms, as well as learn some of the shortcuts behind writing and estimating them. You can also learn how to use your calculator to evaluate logarithms, and learn about a concept called the change of base theory.

### 5. Logarithmic Properties

Along with the change of base property, there are three other logarithmic properties that allow you to manipulate expressions to your advantage. Learn about the product rule, quotient rule and power rule here.

### 6. Practice Problems for Logarithmic Properties

As you get further and further into mathematics, logarithms will appear more and more. It's the point of this lesson to get you used to dealing with them and able to know what to do when you see a whole line of paper full of them!

### 7. How to Solve Exponential Equations

Read this lesson to learn the steps you need to take to solve exponential equations. You'll see that it's not too difficult; you just need to make use of one other mathematical operation in order to solve your problems.

### 8. How to Solve Logarithmic Equations

If you're ever picking out a telescope to see your favorite planet, make sure you do the math first! Learn how to solve the logarithmic equation that will get you the size telescope you want.

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### Other Chapters

Other chapters within the College Mathematics Syllabus Resource & Lesson Plans course

- Math Foundations: College Math Lesson Plans
- Linear Equations: College Math Lesson Plans
- Inequalities: College Math Lesson Plans
- Quadratic Equations: College Math Lesson Plans
- Complex & Imaginary Numbers: College Math Lesson Plans
- Properties of Exponents: College Math Lesson Plans
- Properties of Polynomials: College Math Lesson Plans
- Rational Expressions: College Math Lesson Plans
- Properties of Functions: College Math Lesson Plans
- Logic: College Math Lesson Plans
- Sets: College Math Lesson Plans
- Probability & Statistics: College Math Lesson Plans
- Geometry: College Math Lesson Plans