Section 3.4 - Properties of Logarithmic Functions

Essential Question(s): 

How are the properties of logarithms utilized?

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Follow these three steps to complete this "flip" lesson.

STEP 1: Preparation 
Title your spiral with the heading above and copy the essential question(s).

STEP 2: Vocabulary & Examples 
Copy and define the following of vocabulary. This can be any tables, properties, theorems, terms, phrases or postulates listed. Review the following examples and copy what is necessary for you. Use the guiding questions for your cornell notes.

Properties of Logarithms

• What are the properties of logarithms? (Pg310)
• Review the properties of exponents. (Pg 310 sidebar)
• How can you prove the product rule for logarithms? (Ex 1 pg 310)
• How do you expand the logarithm of a product? (Ex 2 pg 311)
• How do you expand the logarithm of a quotient? (Ex 3 pg 311)
• How do you condense a logarithmic expression? (Ex 4 pg 312)

Change of Base

• What is the purpose of the change-of-base formula for logarithms? (Pg 312-313)
• What is the Change-of-Base Formula for Logarithms? (Pg 313)
• What are the two forms used for the Change-of-Base Formula for Logarithms? (Pg 313)
• How do you evaluate a logarithm by changing the base? (Ex 5 pg 313)

Graphs of Logarithmic Functions with Base b

• How does changing the base of a log function affect the graph of a log function with base b? (Pg 313)
• How can you transform the graph of log functions with base b? (Ex 6 & paragraph below)
• Review the characteristics of logarithmic functions. (pg 314)

Re-expressing Data

• What is a re-expression of data? (Pg 314)
• How can you establish Kepler's Third Law of motion using Logarithmic Re-expression? (Pg 315 & Ex 7)

STEP 3: Reading
Read the following page(s) and take any extra notes as needed.

Overview of Logarithmic Function

• Read pages 310 - 315.
• Make sure to read the paragraphs between the examples.