1. Warm-up: Sketch the graph without your calculator:
p 716 #18, 23 and 27

5. Try this…
Sammy has $1000 she would like to have $4000 dollars to put down on a new car (Sammy says “Who cares about depreciation? I LOVE the smell of a new car!) If she can get continuously compounding interest at 6.5%, how long will it take her to reach her goal of $4000?

6. Okay…so let’s brainstorm.

7. Section 11-4: Logarithmic Functions
Our scintillating questions today are…
How the heck do I solve when my variable is acting as an exponent?
Aren’t logs just hunks of wood?
How do logs behave when you add or subtract them? Multiply or divide? Raise to Powers?
How can I use logs to make my work simpler?
How do you graph a log?

8. Defining an Inverse for Exponential Functions
We will call the inverse a logarithm.
Well, why not? We called the inverse for powers radicals and no one complained.
We abbreviate it as log.
So the inverse of y = e x is…

9. Defining an Inverse for Exponential Functions
We will call the inverse a logarithm.
Well, why not? We called the inverse for powers radicals and no one complained.
We abbreviate it as log.
So the inverse of y = ax is…

10. How do logs work?
First let’s look at its graph:

11. Okay, move it around…

12. Now for something a little confusing…

13. Okay, simpler. It SHOULD equal the exponent.
Remember, that’s what we were trying to solve for.

14. Let’s practice moving from exponential to logarithmic form
Now from logarithmic to exponential.
Okay, let’s solve some.

15. Properties of Logarithms
p 720 in your book.
Let’s prove one…

16. Properties of Logarithms
p 720 in your book.
Let’s prove one…

17. Solve some.

18. Homework:
P A47 Lesson 11-4
Quiz!