# Ch 32: MTEL Math: Exponential & Logarithmic Functions

### About This Chapter

## MTEL Math: Exponential & Logarithmic Functions - Chapter Summary

If you'll soon be taking the MTEL Math exam, review the properties of logarithmic and exponential functions by looking over our interactive lessons. They will give you the skills to better understand:

- Exponential functions and transformations
- Decay vs. exponential growth
- Natural base e
- Understanding and evaluating logarithms
- The inverse of a logarithmic function
- The natural log, logarithms and exponentials
- Shifted and basic graphs of a logarithmic function
- Logarithmic properties
- Solving logarithmic equations
- Exponential growth
- Using the changing-of-base formula
- The behavior of a logarithmic function

Acquiring the right set of skills to effectively solve and work with different functions is easy, thanks to these lessons. Featuring an effective format, they will get you ready for the MTEL Math exam.

### MTEL Math: Exponential & Logarithmic Functions Chapter Objectives

The MTEL Math exam is designed to test your understanding of different functions and their properties so you can get a license in Massachusetts. The content covered in this chapter will be on Subarea 2, which makes up 23% of the entire exam. There are multiple-choice and maybe open-response questions on the exam, which will have you analyze different types of functions.

Our lessons focus on instructing you about different subjects that will be seen on the exam. Since you will have already been exposed to the material, you can address questions comfortably on the exam. Use our self-assessment quizzes to ensure your understanding of different functions and math-related principles.

### 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. 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.

### 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.

### 13. Calculating Rate and Exponential Growth: The Population Dynamics Problem

You know how the world population keeps increasing? It's increasing faster now than it was 100 or 1,000 years ago. In this lesson, learn how differential equations predict this type of exponential growth.

### 14. 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 MTEL Mathematics (09): Practice & Study Guide course

- MTEL Math: Basic Arithmetic Operations
- MTEL Math: Absolute Value & Integers
- MTEL Math: Fractions
- MTEL Math: Decimals
- MTEL Math: Percents
- MTEL Math: Rates & Ratios
- MTEL Math: Proportions
- MTEL Math: Estimation
- MTEL Math: Origins of Math
- MTEL Math: Rational & Irrational Numbers
- MTEL Math: Complex Numbers
- MTEL Math: Properties of Numbers
- MTEL Math: Exponents & Exponential Expressions
- MTEL Math: Roots & Radical Expressions
- MTEL Math: Scientific Notation
- MTEL Math: Number Theory
- MTEL Math: Number Patterns & Sequences
- MTEL Math: Number Patterns & Series
- MTEL Math: Properties of Functions
- MTEL Math: Graphing Functions
- MTEL Math: Factoring
- MTEL Math: The Coordinate Graph & Symmetry
- MTEL Math: Linear Equations
- MTEL Math: Systems of Linear Equations
- MTEL Math: Vectors, Matrices & Determinants
- MTEL Math: Introduction to Quadratics
- MTEL Math: Working with Quadratic Functions
- MTEL Math: Polynomial Functions Basics
- MTEL Math: Higher-Degree Polynomial Functions
- MTEL Math: Piecewise, Absolute Value & Step Functions
- MTEL Math: Rational Expressions, Functions & Graphs
- MTEL Math: Measurement
- MTEL Math: Perimeter & Area
- MTEL Math: Polyhedrons & Geometric Solids
- MTEL Math: Symmetry, Similarity & Congruence
- MTEL Math: Properties of Lines
- MTEL Math: Angles
- MTEL Math: Triangles
- MTEL Math: Triangle Theorems & Proofs
- MTEL Math: Similar Polygons
- MTEL Math: The Pythagorean Theorem
- MTEL Math: Quadrilaterals
- MTEL Math: Circles
- MTEL Math: Circular Arcs & Measurement
- MTEL Math: Analytic Geometry & Conic Sections
- MTEL Math: Polar Coordinates & Parameterization
- MTEL Math: Transformations
- MTEL Math: Data & Graphs
- MTEL Math: Statistics
- MTEL Math: Data Collection
- MTEL Math: Samples & Populations
- MTEL Math: Probability
- MTEL Math: Trigonometric Functions
- MTEL Math: Graphs of Trigonometric Functions
- MTEL Math: Trigonometric Identities
- MTEL Math: Applications of Trigonometry
- MTEL Math: Limits
- MTEL Math: Continuity
- MTEL Math: Rate of Change
- MTEL Math: Derivative Calculations & Rules
- MTEL Math: Graphing Derivatives & L'Hopital's Rule
- MTEL Math: Area Under the Curve & Integrals
- MTEL Math: Integration Techniques
- MTEL Math: Integration Applications
- MTEL Math: Differential Equations
- MTEL Math: Discrete & Finite Math
- MTEL Mathematics Flashcards