1. 11.4 Properties of Logarithms

2. Logarithms A logarithm is an operation, a little like taking the sine of an angle. Raising a constant to a power is called exponentiation. There has to be an “undo” button for exponentiation. Logarithms “undo” exponentials, because a logarithm is the inverse operation to exponentiation.

3. Notation & Forms My notation: The book’s notation:

4. Properties of Logarithms The set-up: Suppose that m and n are positive numbers and b is a positive number other than 1. Let p be any real number. The following properties hold:

5. Product Property

6. Quotient Property

7. Power Property

8. Stop Here

9. Putting it all together Write the following as a sum or difference only:

10. Change of Base Your calculator is NOT smart! Your calculator only does logs in base 10 or base e. What if you had to compute a log in another base? (happens all the time) Change of base formula:

11. When Would I Use a Logarithm? We use logarithms to solve for variable exponents. Example: Solve for x.

12. Example Solve for x.

13. Classwork Pg. 626 # 19-39 [2 each section], 40-46 [3]

14. Homework Pg. 639 # 17, 19, 21, 23, 25-30