2. 1. Eric and Sonja are determining the worth of a $550 investment after 12 years in an account with 3.5% interest compounded monthly. Eric thinks the investment is worth $837.08, while Sonja thinks it is worth $836.57 Are either of them right? 2. A certain plant has a doubling time of 15 days. If there are 58 plants in a field to begin with, how many will there be after a week? How about a month? (With 30 days in it.)

4.  By the end of today, you will be able to… ◦ Understand what logs mean ◦ Evaluate logarithmic expressions ◦ Sketch and analyze graphs of logarithmic functions

5.  The inverse of an exponent is a logarithm  In other words: If f(x) = b x, then f -1 (x) = log b x

6.  How do we test a function to determine whether or not it has an inverse? (unit 2 anyone??)

7.  Domain  Range  Horizontal Asymptote  Y-intercept  End Behavior  If we know that a logarithmic function is the INVERSE, of an exponential function, can we figure out these characteristics of a logarithmic function in general?  Let’s see….

8.  Domain: -∞, ∞  Range: 0, ∞  Intercepts: no x, y = 1  Asymptotes: x-axis (y=0)  End behavior: x -20123 F(x) 1/91/313927 TO FIND THE INVERSE, WE SWITCH X and Y!

9.  Domain:  Range:  Intercepts:  Asymptotes:  End behavior: x 1/91/313927 F(x) -20123

12.  Domain:  Range:  Intercepts:  Asymptotes:  End behavior: x 4211/21/41/8 F(x) -20123

13.  Domain:  Range:  Intercepts:  Asymptotes:  End behavior: x 11/21/41/81/161/32 F(x) -20123

14.  Log functions are the inverse of exponential functions  To find the inverse, you switch x and y.  That means you switch the domain and range, x-intercepts and y-intercepts, and horizontal and vertical asymptotes.

15.  Some of you have a formula from yesterday, others of you have the name of your formula.  There are 5 or 6 per group.  Can you be the first group where all members find each other?  Ready, set, go!

16.  We know they are the inverse of of exponents, but how do they work?  Let’s practice going back and forth between logarithmic and exponential form to see.

17.  log 5 25 = 2  log 4 64 = 3  log 10 10000 = 4  log 7 7 = 1

18.  log 10 100 = 2  log 8 512 = 3  log 3 243 = 5

19.  Common Logarithm: log 10 (log with a base 10) is called a common logarithm and is often written without a base. ◦ So, if you see log50, assume that it means log 10 50  Natural Logarithm: log e (log with a base e) is called a natural logarithm, and is usually written ln ◦ So, if you see ln50, assume that it means log e 50

20.  We use the skill we just practiced to evaluate logarithmic expressions.  Example: Evaluate log 6 36  Set it equal to x  Rewrite as an exponential equation  Determine x

21.  log100000log 9 81

22.  Complete the problems on the back of your guided notes sheet for today.  Working diligently earns you your class work stamp!  I will pass out your homework sheet while you are working on class work

23.  I have lots of papers to return to you today— unfortunately, your tests will not come back to you until Monday.  I need YOU to give me your tracking sheet and exit ticket in my inbox on the way out the door.

24. 1. Will I see you at the Homecoming game tonight? 2. Rewrite the expression in exponential form: log 4 324 3. Evaluate the following expressions: log1000 log 2 ½ 4. Determine the domain, range, x-intercept, and vertical asymptote of y = ln(x – 3)