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Modeling Algebra Fall 2007

Harshbarger & Yocco

Chapter3 Suggestions: (Week 9)

Lab Day: MyMathLab Whew…an easy lab today. If you copied my course, be sure your due dates are appropriate. The assignment is entitled “Week 9.” If you created your own assignment, that of course fine, too.

Day 1: Section 3.2Logarithmic Functions Day 2

Goals for students

  • Understand and work with basic properties of logarithms
  • Understand and work with natural logarithms
  • Write an exponential function in log form and vice versa

You might use today to allow students to work on the worksheets available on the instructor site and then derive the following basic properties from them:

  1. for any base, a >0, where a is any real number
  2. for any base, a >0, where a is any real number
  3. for any base, a >0, where a is any real number

Time permitting, you might work through some of the applications with students and then assign a few for homework as well.

Suggested homework: Finish worksheets started in class.

Selected problems from p. 300: 43 – 69.

Day 2: Section 3.3 Day 1: Properties of Logarithms

Goals for students:

  • Understand the derivation of and use the properties of logarithms

Suggested in-class activity:

Let x = 100 and y = 1000. Find log xy. Make a conjecture about how this value relates to log xand log y? Repeat for x = 10000 and y = 10, then for x = 2 and x = 3. (Use your calculator for this one.). Does your conjecture still hold? Will it always hold? Explain.

Then run through the verification.

Repeat for log .

Then show that log x4 = log = log x + log x +log x +log x =log x. Then generalize.

Forgive the traditional side of me here, but if we want the students to be proficient with these properties, they need to do more than the 4 problems that the text provides.

Suggested homework: Worksheet from Instructor site: Laws of Logs extra practice: selected problems (odds plus a few evens).

Day 3: Section 3.3 Day 2: Exponential equations

Goals for students:

  • Solve exponential equations in context

You might start with the simple exponential equations in example 10 on p. 311, then reinforce by asking students to look at those on the worksheet entitled “Log and exponential equations” on the Instructor site.

Follow up with example 13 on p. 313, then perhaps #52 or #54 on p. 315. The applications supply ample opportunity for students to solve exponential equations.

Suggested homework: p. 314: 1- 10, 31-38, 47- 57 odd

Day 4: Section 3.3 Day 3: Logarithmic equations

Goals for students:

  • Solve logarithmic equations

Suggested homework: p. 314: 39-42 all; Worksheet: parts C (1-9 all) and D (1-6 all)

I’ll probably review on Monday and give the exam during my lab time next week Tuesday.