8.4 Logarithmic Functions 4/8/2013

# 8.4 Logarithmic Functions 4/8/2013

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## 8.4 Logarithmic Functions 4/8/2013

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1. 8.4 Logarithmic Functions 4/8/2013

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

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

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

5. Example 1 24 16 = b. log7 1 0 70 1 = = c. log5 5 1 51 5 = = d. log0.01 2 0.01 = = – 10 2 – e. log1/4 4 1 4 = = – 1 1 – 4 Rewrite Logarithmic Equations logbn = p is bp= n EXPONENTIAL FORM LOGARITHMIC FORM a. log2 16 4 =

6. Checkpoint 34 81 = ANSWER 2. log4 4 1 41 4 = = ANSWER 3. log6 1 0 60 1 = = ANSWER 4. log1/2 4 2 4 = = – ANSWER 2 1 – 2 Rewrite Logarithmic Equations logbn = p is bp= n Rewrite the equation in exponential form. 1. log3 81 4 =

7. Basic Logarithmic Properties Involving One • Logbb = 1 because 1 is the exponent to which b must be raised to obtain b. (b1 = b). • Logb 1 = 0 because 0 is the exponent to which b must be raised to obtain 1. (b0 = 1).

8. Example 2 SOLUTION To help you find the value of logbn, ask yourself what power of b gives you n. a. 4? 64 = What power of 4 gives 64? 43 64 = Guess, check, and revise. log4 64 3 = Evaluate Logarithmic Expressions logbn = p is bp= n Evaluate the expression. a. b. c. log4 64 log4 2 log1/3 9

9. Example 2 1 41/2 2 = Guess, check, and revise. log4 2 = 2 ? 1 c. 9 = What power of gives 9? 3 1 3 2 1 – 9 = Guess, check, and revise. 3 log1/3 9 2 = – b. 4? 2 = What power of 4 gives 2? Evaluate Logarithmic Expressions

10. Evaluate and Simplify Logarithmic Expressions Checkpoint 6 ANSWER . 6. Evaluate log4 ANSWER 1 2 ANSWER 1 16 2 – 5. Evaluate log2 64. 7. Evaluate log16 4.

11. Homework: Prac A WS 8.4