1. Warmup 9/24/15 Do you consider good and evil to be real things? If so, what’s the most good thing you can think of? What’s the most evil? To become familiar with how to change base pp 121: 2, 4, 5, 6 Objective Tonight’s Homework

2. Homework Help Let’s spend the first 10 minutes of class going over any problems with which you need help.

3. Notes on Change of Base What can we do if we want to change the base of a logarithm?

4. Notes on Change of Base What can we do if we want to change the base of a logarithm? Let’s create a proof from a generic example: -We start with a generic equation: y = log a (x)

5. Notes on Change of Base What can we do if we want to change the base of a logarithm? Let’s create a proof from a generic example: -We start with a generic equation: y = log a (x) -Rearrange it as an exponent: a y = x

6. Notes on Change of Base What can we do if we want to change the base of a logarithm? Let’s create a proof from a generic example: -We start with a generic equation: y = log a (x) -Rearrange it as an exponent: a y = x -Take a new log of both sides: log b (a y ) = log b (x)

7. Notes on Change of Base What can we do if we want to change the base of a logarithm? Let’s create a proof from a generic example: -We start with a generic equation: y = log a (x) -Rearrange it as an exponent: a y = x -Take a new log of both sides: log b (a y ) = log b (x) - Pull out the y:ylog b (a) = log b (x)

8. Notes on Change of Base What can we do if we want to change the base of a logarithm? Let’s create a proof from a generic example: -We start with a generic equation: y = log a (x) -Rearrange it as an exponent: a y = x -Take a new log of both sides: log b (a y ) = log b (x) - Pull out the y:ylog b (a) = log b (x) - Isolate y: y = log b (x) / log b (a)

9. Notes on Change of Base What can we do if we want to change the base of a logarithm? Let’s create a proof from a generic example: -We start with a generic equation: y = log a (x) -Rearrange it as an exponent: a y = x -Take a new log of both sides: log b (a y ) = log b (x) - Pull out the y:ylog b (a) = log b (x) - Isolate y: y = log b (x) / log b (a) - So if we set the beginning y equal to the end: log a (x) = log b (x) / log b (a)

10. Group Practice Look at the example problems on pages 89 and 90. Make sure the examples make sense. Work through them with a friend. Then look at the homework tonight and see if there are any problems you think will be hard. Now is the time to ask a friend or the teacher for help! pp 121: 2, 4, 5, 6

11. Exit Question What does doing a calculation with log a even mean? a) The quantity times which the base equals the desired number. b) The number squared which gives the base c) The power to which the base must be raised to give the desired result. d) The value at which the base equals the exponent e) The power to which you must raise the number to get the base f) None of the above