1. More Properties of Logarithms
Section 11.6
More Properties of Logarithms

2. Product Property for Logarithms
Product Property of Logarithms
Property
For
In words: The sum of logarithms is the logarithm of the product of their inputs.
Simplify and write as a sum of logarithms as a single logarithm.
Example

3. Product Property for Logarithms
Using the Product Property for Logarithms
Solution

4. Quotient Property for Logarithms
Quotient Property of Logarithms
Property
For
In words: The difference of logarithms is the logarithm of the quotient of their inputs.

5. Simplify and write as a single logarithms with coefficient of 1.
Quotient Property for Logarithms
Quotient Property of Logarithms
Example
Simplify and write as a single logarithms with
coefficient of 1.
Solution

6. Product Property for Logarithms
Product and Quotient Properties
Solution Continued
Solution

7. Product Property for Logarithms
Product and Quotient Properties
Solution Continued

8. Solving Logarithmic Equation
Solving a Logarithmic Equation
Example
Solve
Solution

9. Solving Logarithmic Equation
Solving a Logarithmic Equation
Solution Continued
There is a negative root of 125/144
The original equation contains 4log5(2x)
Domain of logarithms must be positive
Hence, x must be positive

10. Solving Logarithmic Equation
Solving a Logarithmic Equation
Example
Solve
Solution

11. Solving Logarithmic Equation
Solving a Logarithmic Equation
Solution Continued

12. Change-of-Base Property
For
Find
Use the change-of-base property to write log2(12) in terms of base 10
Example
Solution

13. Use the log key on the calculator to compute
Change-of-Base Property
Converting to log10
Property
Solution Continued
Use the log key on the calculator to compute

14. Change-of-Base Property
Using Change-of-Base Property
Example
Write as a single logarithm.
Use the change-of-base property
Use a graphing calculator to graph
Solution
Example

15. Use the change-of-base property
Using a Graphing Calculator to Solve an Equation in One Variable
Solution
Use the change-of-base property

16. Comparing Properties of Logarithms
Common Error
Warning