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Course: College Algebra
Topic: Exponential and Logarithmic Functions
Subtopic: Properties of Logarithms

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 properties/rules of logarithms down really well. As you work through the material, try to understand why the property/rule holds and what algebraic moves would violate the property/rule.

Objectives

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

• 4.3.1 Understand and be able to apply the basic and "undo" properties of logarithms for any base
• 4.3.2 Understand and be able to apply the product, quotient, and power rules of logarithms for any base
• 4.3.3 Use properties and rules of logarithms to expand, condense, or simplify logarithmic expressions
• 4.3.4 Understand and be able to apply the change of base formula

Terminology

Define: expand vs. condense, change of base

Text Notes

Take note of all the properties and rules given in this section. Have a good note sheet handy for the quiz. The change of base formula is used to convert a logarithm to a ratio of natural logs -- very useful for evaluating logarithmic expressions, graphing logarithmic functions, and solving logarithmic equations.

Supplemental Resources (optional)

If you need supplemental tutorial videos with examples relevant to this section go to James Sousa's MathIsPower4U and search for topic: "Using the Properties Logarithms". Some will be review material from Intermediate Algebra and some will be the more challenging level of this course.