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Course: Algebra III / Intermediate Algebra
Topic: Exponential and Logarithmic Functions
Subtopic: Properties of Logarithms

Overview

Logarithms such as log3x (read "log base 3 of x") have their own algebraic rules. Be sure to memorize the properties of logarithms and the rules of logarithms which define the operations that can be conducted on logarithms as we enter a whole new algebra!

One caution: These rules of logarithms show that, for instance, log(2x) does not equal log(2)*log(x) and log(x+2) does not equal log(x)+log(2). Be careful how you work with logarithms when simplifying logarithmic expressions. Be sure to follow the rules.

Be sure to study logarithms algebraically, graphically, numerically, and electronically. You should be able to evaluate logarithms manually and electronically including utilizing the change of base theorem as necessary.

The change of base theorem will come in handy over and over. Note that it can be written as logbx = log(x)/log(b) or as logbx = ln(x)/ln(b) with the latter being more common. This theorem is vital for entering some logarithms on your calculator. For instance, log415 can be entered as ln(15)/ln(4) ≈ 1.953 (try it).

Objectives

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

• 13.3.1 Know and be able to apply the basic properties of logarithms (memorize them!)
• 13.3.2 Know and be able to apply the product, quotient, and power rules of logarithms (memorize them!)
• 13.3.3 Be able to use the rules of logarithms in both directions "expanding" and "condensing"
• 13.3.4 Understand how and when to use the change of base theorem (memorize it!)
• 13.3.5 Evaluate logarithms algebraically and electronically.

Terminology

Define: product rule of logarithms, quotient rule of logarithms, power rule of logarithms, change of base theorem

Text Notes

MEMORIZE the rules of logarithms (the product rule, the quotient rule, and the power rule) and the basic properties of logarithms. They are sure to appear in "boxes" in your text or take them from the "Logarithm Properties" box on this reference sheet: EE WEb's Algebra Properties Sheet