# Ch 36: MTTC Math (Secondary): Exponential & Logarithmic Functions

### About This Chapter

## MTTC Math (Secondary): Exponential & Logarithmic Functions - Chapter Summary

The lessons in this chapter will help you prepare for the MTTC Mathematics (Secondary) exam by aiding in your review of logarithms and exponents. Watch our expert instructors as they walk you through examples solving math problems with exponential and logarithmic functions. After these lessons you should be better prepared for questions about:

- Exponential growth and decay
- Transformations and graphs of exponential functions
- Evaluating logarithms
- Inverse of logarithmic functions
- Graphing logarithmic functions
- Logarithmic properties
- Solving logarithmic and exponential equations
- Determining the behavior of exponential and logarithmic functions

To ensure you are prepared for the MTTC Mathematics (Secondary) test, be sure to ask our instructors any questions you come up with as you complete these lessons. Following these lesson videos you can complete the lesson assessments to reinforce your understanding of the information presented and discover any topics you haven't mastered.

### 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. 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.

### 4. Using the Natural Base e: Definition & Overview

In this video lesson, you will learn what kind of number 'e' is. Also learn the formal name for this unique number. See what kind of graph the natural base 'e' graphs into, as well as the uses of these types of functions.

### 5. 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!

### 6. 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.

### 7. Writing the Inverse of Logarithmic Functions

Watch this video lesson to learn how inverses are related to the original function. Also learn a method to find the inverse of logarithmic functions that you can easily use.

### 8. Exponentials, Logarithms & the Natural Log

Use the properties of exponentials and logarithms to learn how carbon dating works. This lesson covers properties of a natural log and rules of logarithms.

### 9. Basic Graphs & Shifted Graphs of Logarithmic Functions: Definition & Examples

Watch this video lesson and you will see what the basic graph of the logarithmic function looks like. You will also be able to identify the kind of shifts that will occur by just looking at a logarithmic function when you finish the video.

### 10. 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.

### 11. 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!

### 12. 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.

### 13. 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.

### 14. 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.

### 15. Behavior of Exponential and Logarithmic Functions

After watching this video lesson, you will be able to recognize exponential and logarithmic functions by looking at the end behavior of the graphs. You will also learn how the graphs change.

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### Other Chapters

Other chapters within the MTTC Mathematics (Secondary) (022): Practice & Study Guide course

- MTTC Math (Secondary): Reasoning & Problem Solving
- MTTC Math (Secondary): Basic Arithmetic
- MTTC Math (Secondary): Absolute Value
- MTTC Math (Secondary): Integers
- MTTC Math (Secondary): Introduction to Fractions
- MTTC Math (Secondary): Operations with Fractions
- MTTC Math (Secondary): Introduction to Decimals
- MTTC Math (Secondary): Operations with Decimals
- MTTC Math (Secondary): Percents
- MTTC Math (Secondary): Estimating & Rounding
- MTTC Math (Secondary): Rational & Irrational Numbers
- MTTC Math (Secondary): Complex Numbers
- MTTC Math (Secondary): Properties of Real Numbers
- MTTC Math (Secondary): Exponents & Exponential Expressions
- MTTC Math (Secondary): Roots & Radical Expressions
- MTTC Math (Secondary): Scientific Notation
- MTTC Math (Secondary): Number Theory
- MTTC Math (Secondary): Ratios & Rates
- MTTC Math (Secondary): Proportions
- MTTC Math (Secondary): Vectors, Matrices & Determinants
- MTTC Math (Secondary): Sequences
- MTTC Math (Secondary): Series
- MTTC Math (Secondary): Factoring
- MTTC Math (Secondary): Properties of Functions
- MTTC Math (Secondary): Graphing Functions
- MTTC Math (Secondary): The Coordinate Graph & Graph Symmetry
- MTTC Math (Secondary): Linear Equations
- MTTC Math (Secondary): Systems of Equations
- MTTC Math (Secondary): Inequalities
- MTTC Math (Secondary): Quadratic Equations
- MTTC Math (Secondary): Working with Quadratic Equations
- MTTC Math (Secondary): Polynomial Functions
- MTTC Math (Secondary): Higher-Degree Polynomial Functions
- MTTC Math (Secondary): Piecewise Functions
- MTTC Math (Secondary): Rational Expressions & Functions
- MTTC Math (Secondary): Trigonometric Functions
- MTTC Math (Secondary): Solving Trigonometric Equations
- MTTC Math (Secondary): Limits
- MTTC Math (Secondary): Continuity of a Function
- MTTC Math (Secondary): Rate of Change & Derivatives
- MTTC Math (Secondary): Calculating Derivatives & Derivative Rules
- MTTC Math (Secondary): Graphing Derivatives & L'Hopital's Rule
- MTTC Math (Secondary): Applications of Derivatives
- MTTC Math (Secondary): Area Under the Curve & Integrals
- MTTC Math (Secondary): Integration & Integration Techniques
- MTTC Math (Secondary): Integration Applications
- MTTC Math (Secondary): Differential Equations
- MTTC Math (Secondary): Units & Systems of Measurement
- MTTC Math (Secondary): Perimeter & Area
- MTTC Math (Secondary): Polyhedrons & Geometric Solids
- MTTC Math (Secondary): Symmetry, Similarity & Congruence
- MTTC Math (Secondary): Points, Lines & Angles
- MTTC Math (Secondary): Triangles
- MTTC Math (Secondary): Triangle Theorems & Proofs
- MTTC Math (Secondary): Similar Triangles & Polygons
- MTTC Math (Secondary): The Pythagorean Theorem
- MTTC Math (Secondary): Quadrilaterals
- MTTC Math (Secondary): Circles
- MTTC Math (Secondary): Circular Arcs & Measurement
- MTTC Math (Secondary): Conic Sections
- MTTC Math (Secondary): Polar Coordinates & Parametric Equations
- MTTC Math (Secondary): Transformations
- MTTC Math (Secondary): Types of Graphs, Tables, & Data
- MTTC Math (Secondary): Data & Statistics
- MTTC Math (Secondary): Collecting & Analyzing Data
- MTTC Math (Secondary): Samples & Populations in Research
- MTTC Math (Secondary): Probability
- MTTC Math (Secondary): Discrete & Finite Math
- MTTC Mathematics (Secondary) Flashcards