1. Calculus-9/23/2010 Evaluate using laws of exponents 1) Agenda: 2)
Take Out: Do Now Sheet, Pencil, Homework
DO NOW:
Evaluate using laws of exponents 1) 2)
Agenda:
-Do Now
-HW Questions
-Logs and Exponents powerpoint
HW: Logs and Exponents Handout
Objectives: Solve complex algebraic problems using laws of logs and exponents.
Use the definition of log and exponent to switch between log and exponent form in an algebraic equation.

2. Objectives: Solve complex algebraic problems using laws of logs and exponents. Use the definition of log and exponent to switch between log and exponent form in an algebraic equation.
Exponents, Logs

3. Exponents Exponents are repeated multiplication: n times Example:
Objectives: Solve complex algebraic problems using laws of logs and exponents. Use the definition of log and exponent to switch between log and exponent form in an algebraic equation.

4. Rules for Exponents Rule Example
Objectives: Solve complex algebraic problems using laws of logs and exponents. Use the definition of log and exponent to switch between log and exponent form in an algebraic equation.
Rule Example

5. Practice
Objectives: Solve complex algebraic problems using laws of logs and exponents. Use the definition of log and exponent to switch between log and exponent form in an algebraic equation.

6. More Exponent Rules
Objectives: Solve complex algebraic problems using laws of logs and exponents. Use the definition of log and exponent to switch between log and exponent form in an algebraic equation.

7. Practice
Objectives: Solve complex algebraic problems using laws of logs and exponents. Use the definition of log and exponent to switch between log and exponent form in an algebraic equation.

8. Common Mistakes
Objectives: Solve complex algebraic problems using laws of logs and exponents. Use the definition of log and exponent to switch between log and exponent form in an algebraic equation.

9. ROOTS
Roots don’t count as a separate category, because they are just like exponents. We’ll see why in a second.
Objectives: Solve complex algebraic problems using laws of logs and exponents. Use the definition of log and exponent to switch between log and exponent form in an algebraic equation.

10. Root – Exponent Connection
Objectives: Solve complex algebraic problems using laws of logs and exponents. Use the definition of log and exponent to switch between log and exponent form in an algebraic equation.

11. Practice
Objectives: Solve complex algebraic problems using laws of logs and exponents. Use the definition of log and exponent to switch between log and exponent form in an algebraic equation.

12. Logs Things to Remember…
I want you to be able to use logs to solve for a variable.
Things to Remember…
If you have an exponential equation with a # base use logs to solve.
If you have an exponential equation with base e use natural log (ln) to solve.
Objectives: Solve complex algebraic problems using laws of logs and exponents. Use the definition of log and exponent to switch between log and exponent form in an algebraic equation.

13. Logs Basic Definition of a log:
Objectives: Solve complex algebraic problems using laws of logs and exponents. Use the definition of log and exponent to switch between log and exponent form in an algebraic equation.

14. More Log Rules-Inverse Properties
BASE a:
BASE e:
Objectives: Solve complex algebraic problems using laws of logs and exponents. Use the definition of log and exponent to switch between log and exponent form in an algebraic equation.

15. How can we use this in an algebraic context?
Whenever the variable you are looking for is in the exponent, we need to use logs
Objectives: Solve complex algebraic problems using laws of logs and exponents. Use the definition of log and exponent to switch between log and exponent form in an algebraic equation.

16. Example 2-using inverse property
Objectives: Solve complex algebraic problems using laws of logs and exponents. Use the definition of log and exponent to switch between log and exponent form in an algebraic equation.

17. Example 3- Using Change of Base Rule
Objectives: Solve complex algebraic problems using laws of logs and exponents. Use the definition of log and exponent to switch between log and exponent form in an algebraic equation.

18. Practice-Now you try either use change of base or inverse property to solve for x
e2x = 10
54x + 1 = 15
5 ex + 1 = 30
ex/5 + 4 = 7
32x = 40
Objectives: Solve complex algebraic problems using laws of logs and exponents. Use the definition of log and exponent to switch between log and exponent form in an algebraic equation.

19. Rules of Logarithms Exponents Logarithms
Since a logarithm is simply an exponent which is just being written down on the line, we expect the logarithm laws to work the same as the rules for exponents, and luckily, they do
Exponents Logarithms
bm × bn = bm+n logb xy = logb x + logb y
bm ÷ bn = bm-n logb (x/y) = logb x − logb y
(bm)n = bmn logb (xn) = n logb x
b1 = b logb (b) = 1
b0 = logb (1) = 0
Objectives: Solve complex algebraic problems using laws of logs and exponents. Use the definition of log and exponent to switch between log and exponent form in an algebraic equation.

20. Example 1 Apply product property Change into exponential form to solve
Simplify
Reduce 1 side to zero to solve the quadratic
Factor
Solutions!!
Objectives: Solve complex algebraic problems using laws of logs and exponents. Use the definition of log and exponent to switch between log and exponent form in an algebraic equation.

21. Example 2
Objectives: Solve complex algebraic problems using laws of logs and exponents. Use the definition of log and exponent to switch between log and exponent form in an algebraic equation.

22. Example 3 Product Property of Logs Switch into exponential form
Simplify
Get rid of the fraction by multiplying (x-4)
Solve for x
Objectives: Solve complex algebraic problems using laws of logs and exponents. Use the definition of log and exponent to switch between log and exponent form in an algebraic equation.