Elementary Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems Exponents & Polynomials
Intermediate Algebra
Factoring Rational Expressions Rational Equations and Applications Radical Expressions Nonlinear Equations and Applications Functions and Graphs II Exponential and Logarithmic Functions
Precalculus I / College Algebra
Equations and Inequalitites Functions and Graphs Polynomial and Rational Functions Exponential and Logarithmic Functions Systems and Matrices Geometry Basics Conic Sections Sequences and Series
Precalculus II / Trigonometry
The Six Trigonometric Functions Right Triangle Trigonometry Circular Functions Graphs of Trigonometric Functions Trigonometric Identities Trigonometric Equations Oblique Triangles and the Laws Vectors Complex, Parametric, and Polar Forms
Calculus I
Limits and Continuity Derivatives Analysis of Curves Antiderivatives
Calculus II
Transcendental Functions
Geometry Physics Integration Techniques Calculus of Infinity Parametric, Polar, and Conic Curves
Calculus III

Course: College Algebra
Topic: Exponential and Logarithmic Functions
Subtopic: Logarithmic Functions and Graphs

Overview

Since much of the material in this lesson is review from an intermediate algebra course, our focus here will be to expand on the basic topics, bump-up the level of difficulty, and get logarithmic functions down really well. As you work through the material, try to do what you can algebraically as well as take advantage of technology where appropriate.

Objectives

By the end of this topic you should know and be prepared to be tested on:

• 4.2.1 Understand the basic logarithmic function f(x)=log_b(x) and its graph including being able to produce its graph both manually and that it is the inverse of the function g(x)=b^x
• 4.2.2 Evaluate f(x)=log_b(x) for given values of b and x both manually and electronically
• 4.2.3 Convert from logarithmic form to exponential form and from exponential form to logarithmic form
• 4.2.4 Know the features of the graph of f(x)=log_b(x) including basic shape, domain, range, intercepts, and asymptotes
• 4.2.5 Understand the effects of a, c, and d in y=a*log_b(x-c)+d on the graph of f(x)=log_b(x) including reflections, stretches and shrinks, vertical and horizontal shifts (translations)
• 4.2.6 Understand uses of the common logarithm function log(x) and the natural logarithm function ln(x) including some history of their origins and their applications in science
• 4.2.7 Understand the common and natural logarithmic functions including that they are inverses of the functions 10^x and e^x, respectively
• 4.2.8 Convert common and natural logarithms from from logarithmic form to exponential form and from exponential form to logarithmic form
• 4.2.9 Produce the graphs of the common and natural logarithmic functions both manually and electronically
• 4.2.10 Evaluate the common and natural logarithmic functions for given values of x both manually and electronically

Terminology

Terms you should be able to define: logarithmic function, common logarithm, natural logarithm

Mini-Lectures and Examples

Supplemental Resources (recommended)

Watch video: Logarithms in the Real World

Supplemental Resources (optional)

If you need supplemental tutorial videos with examples relevant to this section go to James Sousa's MathIsPower4U and search for topics below. Some will be review material from Intermediate Algebra and some will be the more challenging level of this course.
"Using the Definition of a Logarithm"
"Evaluating Logarithmic Expressions"
"Graphing Logarithmic Functions"

rev. 2020-10-20