8.4 Logarithmic Functions 4/8/2013

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

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

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

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

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

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).

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

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

Checkpoint 5. Evaluate log Evaluate and Simplify Logarithmic Expressions 6 ANSWER 2 – 7. Evaluate log ANSWER Evaluate log

Homework: Prac A WS 8.4