# Ch 5: Exponential & Logarithmic Functions

### About This Chapter

## Exponential & Logarithmic Functions - Chapter Summary

These lessons will add to your knowledge of exponential and logarithmic functions. Get to know the definition and overview of logarithmic scale, a comparison of exponential growth and decay, plus other subject matter, including:

- Meaning of an exponential function
- Definition and examples of a logarithmic function
- Properties of logarithms
- Exponential function simplifications and solutions
- Solutions for exponential equations and exponential inequalities
- Logarithmic equation solutions
- Exponential and logarithmic function modeling

These short lessons make it easy to make good progress on your studies by using a mobile device to log in from remote locations whenever you have a few minutes to complete a lesson or two. We include a feature that allows you to submit any questions you have to a Study.com expert.

### 1. What Is an Exponential Function?

An exponential function is a function with a variable exponent. Learn about the definition of an exponential function and see some examples and applications of exponential functions in other fields of study.

### 2. Logarithmic Function: Definition & Examples

A logarithmic function is a way to write an exponential function in reverse. Explore the definition and examples of logarithmic functions and learn about exponents vs. logarithms, logarithms in the real world, and natural logarithms used with base 'e.'

### 3. Behavior of Exponential and Logarithmic Functions

Exponential and logarithmic functions are the inverse of one another, the variable being in the exponent in the former and serving as the argument in the latter. Discover the definitions and behavior of these related functions.

### 4. Logarithmic Properties

Including the change of base property, there are four logarithmic properties that allow logs to be manipulated for mathematical applications. Learn why the product and quotient properties require splitting an equation in two and how the power property is used to manipulate exponents.

### 5. Simplifying and Solving Exponential Expressions

Exponential expressions display how many times a number can be multiplied by itself. Learn how to simplify exponential expression problems, examine the functions of an exponent, how it affects positive and negative integers, and solve some sample exponential expressions.

### 6. How to Solve Systems of Logarithmic Equations

In this lesson you will learn some methods that can be used to solve systems of logarithmic equations. Learn how to solve these systems of equations both algebraically and graphically, and then practice your new skills!

### 7. Analyzing Data With Nonlinear Regression Models

There are many nonlinear regression models that can be used to solve a variety of real-world problems. Data in finance, business and physical science can be analyzed using nonlinear regression functions.

### 8. Exponential Growth vs. Decay

Exponential growth and decay are the results of a continuous pattern of numbers found in exponential fractions. Learn more about the differences between exponential growth and exponential decay, and learn how to solve more complex problems by determining a starting value.

### 9. Modeling with Exponential & Logarithmic Functions

This lesson will give a quick review of exponential and logarithmic functions and when to use these functions to model data. Then we will explore the use of graphing calculators in finding exponential and logarithmic functions to model given data.

### 10. Logarithmic Scale: Definition & Overview

A logarithmic scale is a useful way to represent information on a graph, especially when there are exponential changes in the magnitude of the numbers. Learn more, look at several examples and take a quiz to test your knowledge.

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### Other Chapters

Other chapters within the TExES Mathematics/Physical Science/Engineering 6-12 (274): Practice & Study Guide course

- Solving Number Problems
- Advanced Algebraic Functions
- Patterns in Algebra
- Linear & Matrix Algebra
- Trigonometric Functions & Identities
- Differential & Integral Calculus Overview
- 3D Figures & 2D Representations
- Euclidean & Non-Euclidean Geometry
- Geometric Relationships
- Basic Geometric Figures
- Transformational Geometry
- Data Display Methods
- Data Measurement
- Probability Theory
- Proofs & Reasoning in Math
- Applications of Mathematics
- Mathematical Instruction
- Student-Centered Math Instructional Strategies
- Mathematical Assessments
- Scientific Instruments & Measurements
- Safety Procedures and Hazards in Scientific Research
- Data Collection & Communication
- Nature & Impact of Science
- Systems in Science
- Scientific Models
- Motion in One Dimension
- Two-Dimensional Motion and Vectors
- Applications of Electricity & Magnetism
- Work, Power & Energy
- Momentum & Conservation
- Heat Energy & Thermodynamics
- Wave Behavior in Physics
- Matter & Atomic Structure
- Fundamentals of Quantum Physics
- Gas Laws & Properties
- Properties of Ionic & Covalent Bonds
- Chemical Equations & Reactions
- Solution Types & Properties
- Energy Forms & Transformations
- Nuclear Fission, Fusion & Reactions
- Oxidation & Reduction Reactions
- Acids, Bases & Reactions
- Science Instruction & Assessment
- Engineering Processes & Tools
- Fundamentals of Stress & Strain
- Temperature & Heat in Engineering
- Basics of Structural Engineering
- Tolerance in Engineering
- Pressure in Engineering
- Math, Science & Economics in Engineering Design
- The Role of Information Technology in Engineering
- Engineering in Context
- Ethical & Legal Requirements of the Engineering Profession
- Engineering in the Classroom & School Community
- TExES Math/Physical Science/Engineering 6-12 Flashcards