1. 8.4 Logarithmic Functions 4/8/2013

2. Definition of a Logarithmic Function log b n = p is equivalent to b p = n (logarithmic form) (exponential form)

3. Location of Base and Exponent in Exponential and Logarithmic Forms Logarithmic form: p = log b n Exponential Form: b p = n Exponent Base

4. Popular Bases have special names Base 10 log 10 x = log x is called a common logarithm Base “e” log e x = ln x is called the natural logarithm

5. Example 1 Rewrite Logarithmic Equations LOGARITHMIC FORM a. log 2 16 = EXPONENTIAL FORM 42424 = 16 b. log 7 1 = 0 7070 = 1 c. log 5 5 = 1 5151 = 5 d. log 0.01 = 2 – = 0.0110 2 – e. log 1/4 4 = 1 – = 4 4 1 – 1 log b n = p is b p = n

6. Checkpoint Rewrite the equation in exponential form. Rewrite Logarithmic Equations 1. log 3 81 = 4 ANSWER 3434 = 81 2. log 4 4 = 1 3. log 6 1 = 0 4141 = 4 ANSWER 6060 = 1 log 1/2 4 4. = 2 – = 4 2 1 – 2 ANSWER log b n = p is b p = n

7. Basic Logarithmic Properties Involving One Log b b = 1 because 1 is the exponent to which b must be raised to obtain b. (b 1 = b). Log b 1 = 0 because 0 is the exponent to which b must be raised to obtain 1. (b 0 = 1).

8. Example 2 Evaluate Logarithmic Expressions Evaluate the expression. a. log 4 64 b. log 4 2 c. log 1/3 9 SOLUTION To help you find the value of log b n, ask yourself what power of b gives you n. a. 4?4? = 64 What power of 4 gives 64 ? 4343 = 64 Guess, check, and revise. log 4 64 = 3 log b n = p is b p = n

9. Example 2 Evaluate Logarithmic Expressions 4 1/2 = 2 Guess, check, and revise. log 4 2 = 2 1 = 9 3 1 – 2 Guess, check, and revise. c. = 9 3 1 What power of gives 9 ? ? 3 1 log 1/3 9 = 2 – b. 4?4? = 2 What power of 4 gives 2 ?

10. Checkpoint 5. Evaluate log 2 64. Evaluate and Simplify Logarithmic Expressions 6 ANSWER 2 – 7. Evaluate log 16 4. ANSWER 2 1 6. Evaluate log 4 16 1.

11. Homework: Prac A WS 8.4