1. During this lesson, you will: Write and evaluate logarithmic expressions Graph logarithmic functions Use logarithms in real-life situations Logarithmic Functions

2. Part One: Writing and Evaluating Logarithmic Functions

3. Evaluating Logarithmic Functions We know that 2 2 = 4 and 2 3 = 8, but for what value of y does 2 y = 6? Because 2 2 < 6 < 2 3, we would expect the answer to be _____________. To answer this question more precisely, mathematicians invented ___________. between 2 and 3 logarithms

4. Definition: Logarithm Definition of Logarithm to Base b The logarithm of y with base b is denoted by log b y and is defined as follows: log b y = x iff b x = y. The expression log b y = x is read as “log to the base b of y = x.”

5. Location of the Base and Exponent in Logarithmic and Exponential Forms Logarithmic Form: log b y = x Exponential Form: b x = y EXPONENT BASE EXPONENT Note: A logarithm is an exponent.

6. Example 1 Rewriting Exponential and Logarithmic Equations Logarithmic FormExponential Form log 2 16 = __________ log 10 10 = __________ log 3 1 = __________ Log 10 0.1 = __________ log 2 6 =2.585 2 _____ = _____ 3 -4 = _____ 4 3 = _____ 5 4 = _____ 10 -3 = _____ 4 2 4 = 16 110 1 = 10 03 0 = 1 10 -1 = 1/10 =0.1 1/81 log 3 1/81 = -4 2.585 6 64log 4 64 = 3 625log 5 625 = 4 0.001log 10.001 = -3

7. ALERT!A logarithm is an exponent. To evaluate log 3 9, you would ask “____________________”? 3 to what power is 9

8. Example 2 Evaluating Logarithms a. log 4 16b. log 5 1log 4 2log 3 (-1) 02 undefined 1/2

9. Not-So-Special Logarithmic Values 1.log a 1=______ Because: 2. log a a =______ Because: 3. log a a x =______ Because: Let a and x be positive number such that a ≠ 1, 0 a 0 = 1 1 a 1 = a x a x = a x

10. Example 3 Using a Calculator to Evaluate a Logarithm log 2 6 = ________ Using the change of base formula, you can write log 2 6 = log 10 6 = log 10 2 log 2.584

11. Homework Assignment: Day 1: Text, page 442: 6-25 all, 50, 53-61 all. Plus, evaluate the following using a calculator: log 3 20log 4 7log 1.4 10log 6 (-3)