## Section 3.5 - Equation Solving and Modeling

**Essential Question(s):**

How are logarithms used with modeling and solving application problems?

**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.

__Solving Exponential Equations__

- What are the one-to-one properties between exponential and logarithmic functions? (pg 320)
- How do you solve an exponential equation algebraically? (Ex 1 pg 320)
- How do you solve an exponential equation graphically? (Ex 2 pg 321)

__Solving Logarithmic Equations__

- What must you keep track of when solving logarithmic equations? (pg 321)
- How do you solve a basic logarithmic equation? (Ex 321 & pg 321-322; look at paragraph after)
- How do you solve a logarithmic equation? (Ex 4 pg 321)

__Orders of Magnitude and Logarithmic Models__

- What is an order of magnitude? (Pg 323)
- How are orders of magnitude used? (Pg 323-324)
- How can you compare Earthquake intensities? (Ex 5 pg 324)
- How can you compare Chemical acidity? (Ex 6 pg 325)

__Newton's Law of Cooling__

- What is Newton's Law of Cooling? (pg 326)
- How do you apply Newton's Law of Cooling? (Ex 7 pg 326-327)
- What is another form of Newton's Law of Cooling and when it is used? (Pg 327)
- How do you model with Newton's Law of Cooling? (Ex 8 pg 327)

__Logarithmic Re-expression__

- What are the regression models related by Logarithmic Re-Expression? (pg 328-329)
- How do you use the appropriate regression model? (Ex 9 pg 330)

**STEP 3: Reading**

__Read__the following page(s) and take any extra notes as needed.

- Read pages 320 - 330.
- Make sure to read the paragraphs between the examples.