# Ch 15: NYSTCE Mathematics: Exponential & Logarithmic Functions

### About This Chapter

## NYSTCE Mathematics: Exponential & Logarithmic Functions - Chapter Summary

Restore your memories about exponential and logarithmic functions by looking through these helpful video lessons. Doing well on the NYSTCE Mathematics Test requires that you have a strong background in the major fields of mathematics, particularly algebra, so use our study materials to make sure you know about the following:

- Definitions of logarithms and exponential functions
- Decay vs. exponential growth
- Formulas to determine compounding interest
- Techniques for analyzing logarithms
- Logarithmic properties and practice equations
- Strategies for solving exponential and logarithmic equations
- Effects and transformations on range/domain of graphed logarithms
- Logarithms and the Change-of-Base formula

Many of the topics you will need to know for the NYSTCE Mathematics Test are basic concepts you probably learned during your high school mathematics classes. While you might understand how to solve these types of problems, you may not remember all the related terms or finer points. Let this chapter give you a full recap of all the major topics. We offer you quick lessons that keep you entertained as you review the information. Whether you watch all of the lessons or only the ones you need is completely up to you, and you can watch any lesson as many times as you want. There are even quizzes attached to every lesson, so you can easily determine how well you know the material that will be on the test.

### 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. Compounding Interest Formulas: Calculations & Examples

Compound interest is a great way to have your money work for you. In this lesson, find out the formula for calculating compound interest and practice using the formula with several examples.

### 4. 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!

### 5. 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.

### 6. 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.

### 7. 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!

### 8. 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.

### 9. 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.

### 10. How to Graph Logarithms: Transformations and Effects on Domain/Range

The graph of a basic logarithm is relatively simple. This lesson will show you how to graph a logarithm and what the transformations will do to the graph as well as their effects on the domain and range of the graph.

### 11. Transformation of Exponential Functions: Examples & Summary

All exponential functions follow a basic graph. But when you make changes to the function, you will see the graph shift and make changes. Watch this video lesson to learn how to easily identify these changes or transformations.

### 12. Using the Change-of-Base Formula for Logarithms: Definition & Example

Logarithms have many uses in the real world. But what happens when the calculation uses a base other than the standard base 10? Watch this video to find out how to handle this situation and the formula to use.

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### Other Chapters

Other chapters within the NYSTCE Mathematics (004): Practice & Study Guide course

- NYSTCE Mathematics: Fractions, Decimals & Percents
- NYSTCE Mathematics: Complex Numbers
- NYSTCE Mathematics: Factoring & Divisibility
- NYSTCE Mathematics: Exponents
- NYSTCE Mathematics: Patterns & Functions
- NYSTCE Mathematics: Understanding Algebraic Expressions
- NYSTCE Mathematics: Solving Algebraic Equations
- NYSTCE Mathematics: Linear Equations
- NYSTCE Mathematics: Quadratic Functions
- NYSTCE Mathematics: Polynomial Functions
- NYSTCE Mathematics: Exponential Expressions
- NYSTCE Mathematics: Absolute Value Expressions
- NYSTCE Mathematics: Rational Expressions
- NYSTCE Mathematics: Radical Expressions
- NYSTCE Mathematics: Trigonometry
- NYSTCE Mathematics: Applications of Trigonometry
- NYSTCE Mathematics: Calculus Concepts
- NYSTCE Mathematics: Calculus Applications
- NYSTCE Mathematics: Principles of Measurement
- NYSTCE Mathematics: Lines & Angles
- NYSTCE Mathematics: Parallel Lines & Symmetry
- NYSTCE Mathematics: Geometric Construction
- NYSTCE Mathematics: Geometric Shapes
- NYSTCE Mathematics: Triangle Proofs & Theorems
- NYSTCE Mathematics: Geometric Solids
- NYSTCE Mathematics: Conic Sections
- NYSTCE Mathematics: Vector Operations
- NYSTCE Mathematics: Transformations in Geometry
- NYSTCE Mathematics: Coordinate Geometry
- NYSTCE Mathematics: Sequences & Series
- NYSTCE Mathematics: Counting Strategies
- NYSTCE Mathematics: Probability
- NYSTCE Mathematics: Probability Distributions
- NYSTCE Mathematics: Data Analysis & Statistics
- NYSTCE Mathematics: Sampling & Prediction
- NYSTCE Mathematics: Regression & Correlation
- NYSTCE Mathematics: Discrete Mathematics
- NYSTCE Mathematics Flashcards