1. 8 – 4 : Logarithmic Functions (Day 1) Objective: Be able to evaluate Logarithmic Functions.

3. Let b and y be positive numbers b ≠ 1. The logarithm of y base b is denoted by Log b y and is defined as follows: Definition of Logarithm with Base b

4. logarithmic formexponential form

5. Example 1: Rewriting Logarithmic Expressions A.) log 2 32 = 5 2 5 = 32 B.) log 5 1 = 0 5 0 = 1 C.) log 10 1 = 1 10 1 = 10 10 -1 = 0.1 D.) log 10 0.1 = -1 (1/2) -1 = 2 E.) log 1/2 2 = -1

6. Special Logarithm Values Let b be a positive real number such that b ≠ 1

7. Example 2: Evaluating Logarithmic Expressions Evaluate the expression. 3 raised to what power equals 81? x 3 x = 81

8. 5 raised to what power equals 0.04? x 5 x = 0.04

9. ½ raised to what power equals 8? 9 raised to what power equals 3?

10. ln and e are inverses of each other

11. Example 3: Evaluating Common and Natural Logarithms

12. Homework: P. 490 #16 – 34 even, 36 -47 all

13. Example 4: Evaluating a Logarithmic Function The slope s of a beach is related to the average diameter d (in millimeters) of the sand particles on the beach by this equation. Find the slope of a beach if the average diameter of the sand particles is 0.25 millimeters.

14. Solution If d = 0.25, then the slope of the beach is: