Algebra 2 Note-taking Guide
Algebra 2 - Lesson 7.03 Properties of Logarithms
Please print this out in advance, and as you are working through the lesson, fill in the information and use this as your notes.
þ The goal is to have all the empty boxes checked
As you complete this lesson, please check that you can answer:
¨ I know how the properties of logarithms can be applied to simplify or solve equations.
¨ I know the types of scenarios where the change of base formula can be helpful.
Change of Base Formula with the Common Logarithm (Page 2)
In the logarithmic expression log28, the small 2 in the corner of the log is called the ______and the 8 is called the ______.
Review how to evaluate the expression:
¨ Yes, I have reviewed how we can evaluate log28.
The change of base formula allows you to find the value of a logarithm with a base other than 10 using a calculator. Divide the common logarithm of the ______by the common logarithm of the ______.
Change of Base Formula with the Natural Logarithm (page 2)
A log of baseeis called the ______log. It is written as "ln" followed by the argument. It is possible to find the value of a natural log expression by using the Change of Base formula. However, instead of using the common log within the fraction, you'll use the natural log.
Change of Base Formula with Other Bases (page 2)
The Change of Base Formula can also be used to rewrite a given logarithm using another base. For example, to rewrite the logarithmic expression log2781 using base 3, the argument, 81, is written in the numerator of the fraction. The base, 27, is in the denominator. The only difference is that a log with base 3 will be used instead of the common log.
When the base of a logarithm is the same as its argument, the solution will always be 1. Since the base and the argument are the same, the numerator and denominator will also be the same.
Use the space below to complete examples 1-3 on page 2:
Example 1 /Example 2 /
Example 3 /
Properties of Logarithms (pages 3-4)
Recall:
Review the properties on pages 3-4 and summarize each in the table below:
Property Name / Rule in Symbol Form / Example(s)The Equality Property
The Product Property
The Quotient Property
The Power Property
Now let’s apply all of these properties. Complete examples 1-3 from page 4 in the space below:
Solving Logarithmic Equations with Constants (page 5)
Do you remember how to solve logarithmic equations such as log7x = 3?
You learned how to solve this equation by converting it into an exponential equation. Remember BNE BEN
When you encounter a logarithmic equation where constants are involved, isolate the constants on one side. Isolate the logarithms on the other side. Then, turn the logarithmic equation into an exponential equation.
(Find this example by clicking on “Learn More” at the bottom of page 5.
Practice (Page 6)Practice (Page 7)
You Try 1 (Page 8)
You Try 2 (Page 8)
You Try 3 (Page 8)
You Try 1 (page 9)
You Try 2 (page 9)
You Try 3 (page 9)
Finally, complete the 7.03 Assessment, Properties of Logarithms. This is an auto-graded assignment. You will get immediate feedback on your work.
Algebra 2 Notetaking Guide
Version 14
Florida Virtual School