1. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Objectives Simplify and evaluate expressions involving logarithms. Solve equations involving logarithms. 6.4 Properties of Logarithmic Functions

2. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Glossary Terms exponential-logarithmic inverse properties one-to-one property of logarithms power property of logarithms product property of logarithms quotient property of logarithms 6.4 Properties of Logarithmic Functions

3. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Rules and Properties Properties of Logarithms 6.4 Properties of Logarithmic Functions Product Property log b (mn) = log b m + log b n For m > 0, n > 0, b > 0, and b  1:

4. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Rules and Properties Properties of Logarithms 6.4 Properties of Logarithmic Functions Quotient Property log b = log b m – log b n m n For m > 0, n > 0, b > 0, and b  1:

5. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Rules and Properties Properties of Logarithms 6.4 Properties of Logarithmic Functions Power Property log b m p = p log b m For m > 0, n > 0, b > 0, and any real number p:

6. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Rules and Properties Exponential-Logarithmic Inverse Properties log b b x = x 6.4 Properties of Logarithmic Functions For b > 0 and b  1: b log x = x b and for x > 0

7. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Rules and Properties One-to-One Property of Logarithmic Functions If log b x = log b y, 6.4 Properties of Logarithmic Functions then x = y.

8. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Key Skills Use the Product, Quotient, and Power Properties of logarithms to simplify and evaluate expressions involving logarithms. 6.4 Properties of Logarithmic Functions given: log 5 12  1.5440 log 5 10  1.4307 a. log 5 120 = log 5 (12  10) = log 5 12 + log 5 10  1.5440 + 1.4307  2.9747

9. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Key Skills Use the Product, Quotient, and Power Properties of logarithms to simplify and evaluate expressions involving logarithms. 6.4 Properties of Logarithmic Functions given: log 5 12  1.5440 log 5 10  1.4307 b. log 5 1.2 = log 5 12 – log 5 10  1.5440 – 1.4307  0.1133 = log 5 12 10

10. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Key Skills Use the Product, Quotient, and Power Properties of logarithms to simplify and evaluate expressions involving logarithms. 6.4 Properties of Logarithmic Functions given: log 5 12  1.5440 log 5 10  1.4307 c. log 5 125 4 = 4  3 = 12 = 4 log 5 125 TOC