About This Chapter
Logarithmic & Exponential Functions - Chapter Summary
This engaging chapter fully explains logarithmic and exponential functions. Topics covered in these fun lessons include rational exponents, the five main exponent properties and the definition of a logarithm. You'll also review logarithmic properties, exponentials and the natural log and examples of both the basic and shifted graphs of logarithmic functions. Other lessons explain differentiation and integration as they relate to composite functions. After completing this chapter, you should be ready to:
- Describe the behavior of logarithmic and exponential functions
- Explain the proof for the change of base formula
- Calculate derivatives of exponential and logarithmic functions
Tackle even the toughest of subjects with our helpful, user-friendly video and text lessons. Our professional instructors have created these materials to make it easy and fun to learn at your own pace. Each lesson is accompanied by a short multiple-choice quiz that helps you identify the subjects that need more study. If any of the topics are confusing, contact one of our instructors for assistance.
1. Rational Exponents
In this video, learn how to go from a rational exponent to a radical expression and back. No tricks or magic, just good math! We'll review the basics and look at a few examples.
2. What Are the Five Main Exponent Properties?
We'll look at the five important exponent properties and an example of each. You can think of them as the order of operations for exponents. Learn how to handle math problems with exponents 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. 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.
5. 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.
6. 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.
7. 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.
8. Change Of Base Formula: Logarithms & Proof
Logarithmic expressions are frequently written with a base that can not be simplified easily. When this happens, you can use the change of base formula to change the base to something that can be worked with. This lesson will show you how to do that, and give some examples followed by a quiz.
9. Calculating Derivatives of Exponential Equations
Earth's population is booming! But why is the population increasing so much more drastically than it did many years ago? In this lesson, learn how to calculate the rates of change in exponentials by discovering the rules of derivatives with exponents.
10. Calculating Derivatives of Logarithmic Functions
Logarithms appear in all types of applications like carbon dating, brightness of stars and musical acoustics. In this lesson we explore how to calculate the derivative of logarithmic functions.
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Other chapters within the HSC Mathematics: Exam Prep & Syllabus course
- Mathematical Proofs & Reasoning
- Basic Arithmetic & Algebra
- Factorization of Binomials & Trinomials
- Types of Equations & Inequalities
- Plane Geometry
- Circle Plane Geometry
- Probability & Randomization
- Arithmetic & Geometric Series
- Trigonometric Ratios
- Geometrical Representations of Functions
- Linear Functions & Lines
- Derivatives of Functions
- Quadratic Polynomials & Parabolas
- Geometrical Applications of Differentiation
- Calculating Trigonometric Functions
- Understanding Inverse Functions
- Factoring & Graphing Polynomials
- Roots & Coefficients of Polynomials
- Binomial Theorem & Probability
- Graphing & Solving Functions
- Solving & Graphing Complex Numbers
- Geometric Representations of Complex Numbers
- Square Roots, Powers & Roots of Complex Numbers
- Conic Sections Basics
- The Ellipse in Algebra
- The Hyperbola
- The Rectangular Hyperbola
- Calculus Applications: Rate of Change
- Calculus Applications: Velocity & Acceleration
- Calculus Applications: Projectile & Harmonic Motion
- Calculus Applications: Resisted Motion
- Calculus Applications: Circular Motion
- HSC Mathematics Flashcards