2. 2 x = 42 y = 82 z = 6 X = 2y = 3 Z = ? Mathematicians use a LOGARITHM to find z and we will study logarithmic functions this unit A logarithm is the inverse of an ______________ function Exponential

3. Inverses These 2 graphs are reflections over the line _________ XY -3 -2 0 1 2 3 XY -3 -2 0 1 2 3 y = x 1/8 1/4 1/2 1 2 4 8 1/8 1/4 1/2 1 2 4 8 Note exp fcn has H.A. and log fcn has V.A.

4. If x = b y then ________ Look at the log function graph: x > 0 log b x = y always greater than 0x is ____________________ domain is _________ Value of asymptote

5. If x = b y then ________ log b x = y Convert the Exponential Equations to Logarithms 1. 2. 3. 3 2 = 9 log 2 16 = 4 log 10 100 = 2 log 3 9 = 2 Note that we are changing form …. not solving

6. If x = b y then ________ log b x = y Convert the Exponential Equations to Logarithms 4. 5. 6. 1 = 5 0 log 4 = -2 log 10 0.1 = -1 log 5 1 = 0

7. If x = b y then ________ log b x = y Write the Logarithmic Equations in Exponential Form 7. 8. 9. log 8 64 = 2 log 2 8 = 3 log 100 = 2 When no base is written ….it is a common log with base 10

8. If x = b y then ________ y = log b x Evaluate each Logarithm 1. 2. =x 3. log 1000 = x log 3 27 = x log 6 Now we are solving for x

9. If x = b y then ________ y = log b x Evaluate each Logarithm 4. 5. =x 6. log 8 16 =x log 9 27 = x log ½

10. Special Logarithm Values log b 1=_____log b b=_____log b b x =_____ b x = 1 0 b x = b 1 b x = b x x Why are these good rules to know: (not on your notes) Find the y-intercept of Substitute 0 for x (0,4)

11. For example: log x = _____________ (The log key on the calc. is the common log) 10 log 10 x

12. Use the change of base Formula : log b x = Example: log 2 7 =

13. Vertical Shift: Parent Function: Horizontal Shift: Stretch/Compress: Reflection in x-axis: The k The h

14. On an earlier slide we graphed an exponential function and its inverse. This current slide is not in your notes – but lets prove why y=2 x and y = log 2 x are inverses. y = log 2 x x = log 2 y Switch variables to find inverse equations Convert from log to exp. form

15. Look above at the parent function of y = log 2 x Left 1 Horiz shift ________ Vert Shift = _______ V Asymptote: ______ Domain: __________ Up 4 x = -1 Parent Function Y=log 2 x XY 1/4 -2 1/2 10 21 42 83 4 1 X-intercept:______ 0 = log 2 (x+1) +4 – 4 = log 2 (x+1) 2 - 4 = x+1 x > -1

16. Activity: Now lets see what you know. I will show you some problems. When I ask for the answer, please show the color of the matching correct answer. HW : WS 8.2 – which is is due next class. We will also be taking a quiz next class on these concepts.

17.  A. log 2 4=16  B. log 2 16=4  C. log 4 16=2  D. log 16 4=2

18.  A. log b c=a  B. log c b=a  C. log a b=c  D. log a c=b

19.  A. b c =a  B. a c =b  C. a b =c  D. b a =c

20.  A. 3 9 =2  B. 2 3 =9  C. 3 2 =9  D. 9 2 =3

21.  A. 3  B. 4  C. 16  D. 256

22.  A. -4  B. -3  C. 3  D. 4

23.  A. -4  B. -27  C. 27  D. 243

24. A. Translated down 1 and left 5 B. Translated up 1 and left 5 C. Translated left 1 and down 5 D. Translated right 1 and down 5

25. A. X 1 B. X 1 C. X -1 D. X -1

26. A. (7,0) B. (8,0) C. (9,0) D. (10,0)

27. A. X=1/3 B. X=27 C. X=-2 D. X=-27

28. A. X=-5 B. X=-3 C. X=3 D. X=7

29. A. X=1.5 B. X=5 C. X=6 D. X=9

30. A. X=10/3 B. X=4 C. X=16 D. X=64

31. A. X=-81 B. X=9 C. X=2/3 D. X=3/2

32. A. X=-27 B. X=-9 C. X=-4 D. X=27

33.  Like HW 8.2