## Section 3.4 - Properties of Logarithmic Functions

**Essential Question(s):**

How are the properties of logarithms utilized?

**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.

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