1. Properties of Logarithms
Keeper 38
Honors Algebra II

2. Logarithms of Products
The Product Rule loga MN = loga M + loga N The logarithm of a product is the sum of the logarithms of the factors

3. Example
Express as a single logarithm:

4. Logarithms of Powers
The Power Rule The logarithm of a power of M is the exponent times the logarithm of M

5. Example
Express as a product.

6. Example
Express as a product.

7. Example
Express as a product.

8. Logarithms of Quotients
The Quotient Rule The logarithm of a quotient is the logarithm of the numerator minus the logarithm of the denominator

9. Example
Express as a difference of logarithms:

10. Example
Express as a single logarithm:

11. Example – Putting it all together!
Express each of the following in terms of sums and differences of logarithms.

12. Example - Putting it all together!
Express each of the following in terms of sums and differences of logarithms.

13. Example - Putting it all together!
Express each of the following in terms of sums and differences of logarithms.

14. Example - Putting it all together!
Express as a single logarithm:

15. You try

16. Example

18. Examples

19. Examples

20. Examples

21. Expressions of the Type
A Base to a Logarithmic Power The number a raised to the power loga x is x

22. Example
Simplify.

23. Example
Simplify.

24. Example
Simplify.