1. Chapter 8 Section 3 Exploring Logarithms Algebra 2 Notes May 1, 2009 This Slide Show Comes to you Courtesy of Mr. Callahan! Modifications Done by Yours Truly

2. What’s a logarithm? Think of a logarithm as an exponent! Yes; A logarithm is a another way of writing exponential functions! Righteous! Mine?

3. How the heck did that happen? The Inverse Function

4. We need a little more background on logarithms! Exponential FunctionLogarithmic Function exponent base exponent base Argument TASTEY!!!

5. Special types of Logarithms: Common Logarithm: A logarithm with base 10. Natural Logarithm: A logarithm with base e. Log 10 1000 = 3 Ln e 1.649 = 1/2

6. Now you try some! Write each exponential equation as a logarithm. Write each logarithmic equation as an exponential. Log 4 8 = 3/2 Log 10 1/100 = -2 Ln e -1 = ∏i 4 3 = 6410 1.6 = 40 e 2 = e 2

7. Solve. Round decimal answers to the nearest hundredth. x -4 = 16 Well 2 -4 = 1/(2) 4 = 1/16, so then turn it into ½ x = ½ Log 10 34 =x Log 34 = 1.5315 Check answer 10 1.531478917 = 34! e x = 23.5 Ln e 23.5 = x Ln 23.5 = 3.157 Check answer e 3.157 = 23.4999

8. Dude, logarithms are totally cool! Just wait; it gets even better!

9. Homework #58 Page 450 #6, 10-12, 14-17, 19, 20, 22, 24, 35, 40, 54, 67, 68