Notes ÿ.3 Log Functions and Graphs 2014-15.notebo6k February 10, 2015

Can you figure out the pattern?

log4 1 m -2

og8 8 1

I0 log, R -1

Notes 8.3 Log Functiohs and Graphs 2014-15.notebook ' February 10, 2015

Notes 8.3:

Log Functions

en ogby = b -7' l and b > O.

2

Notes 8.3 Log Functions and Graphs 2014-15.notebook February'10, 2015

JS" ' ))

Write the tollowinexponential form.

equations in

log2128 im 7 1

Notes 8.3 Log Functions and Graphs 2014-15.notebooÿ February 10, 2015

Write the following equations in logarithmicform:

1, 25 = 52 2. 729 = 3ÿ

4

Notes 8.3 Log Functiorÿs and Graphs 2014=15.notebook ' February 10, 2015

Evaluate the following logs:

log39 :ÿ log77 ÿ ,ÿ: log51

+

log816 132

f ?"

X

5

Notes 8.3 Log Functions and Graphs 2'014-15.notebook February'10, 2015

Find the inverse of the given gÿrap]h.

!0

86

14

x

-!0 -8:6 -4

-6

=10

24 6-2 // ÿ2

4

8 10

/

6

Notes 8.3 Log Functions and Graphs 2014-15.notebook February 10, 2015

Find the inverse of y = log4x./

A log ÿunetion is the inverse of an

exponential. How will the ÿraphs compare?

i>; ÿt;ÿ

6 6 7 9

7

Notes 8.3 Log Function's and Graphs 2014-15onotebook ' February 10, 2015

Graph y = log2 xq bÿ

\'¢ S' av O

jJÿzy

2

4

i : /

-2 -1

:2

345678910i I ! ÿ i i

8

Notes 8.3 Log Functions and Graphs 2014=IS.notebook February ÿ0, 2015

Graph y = log5 (x + 3) - 1

,jJ

t i t i i-2 .1ÿ-¸-5 -!

-;-2

I ' !-3

i.5

5 -

2

i.

4 52 3

12

Notes 8.3 Log Functions and Graphs 2014-15.notebook February ÿ!0, 2015

Graph y = leg x

i/i?jII0 ..........

io6 ........

i !!: i8! i7!. 1.6

" 4,

I

-2 -! 4

!.2

' i I !

_ ! i i i i

i• ÿ '> i ; lf!

"i , i .... !J

4j

Notes 8.3 Log Functions and Graphs 2014-15.noteboolÿ February 10, 2015

;i) :;-'ÿ, ,¢;%

i

10

Notes 8.3 Log Function's and Graphs 2014-15.notebook ' February 10, 2015

Another way to graph legs is by using translations.

Graph y = log6 (x- 2) + 3 Z, ÿ

, 3

I I-2 -!

i -2

i ÿ-4-

"5

I1

i

i t J4 5 6 7 8

! i

11

Notes 8.3 Log Functions and Graphs 2014-15.notebook February 10, 20t5

Write each equation in logarithmic form.

6. 49 =72 7.103 = 1000

10. 8?, = 64 1.1,.4 = (½)-2

Evaluate each logarithm.

14. log2 16 15. log 4 2

18. lo,,ÿz 8 19. log 49 7

122. l%2 25 23. log½

Graph each logarilhmic function.

38. y = log4 x 36. 3; = log.5 x

38. y = log5x + 1 39. v- log7(x-2)

Write each equation in exponential form.

53. tog2 128 .... 7 54. log 0,0001 = -4

56. I%66 = l 57,1og41 = 0

59. log2 ½ = -i 60. log 1() = 1

Find tile inverse of each thnction.

64. y= log4x 65. y= log0,sX

67. 3' = log2 2x 68. y = log (x + 1)

70. y = log(x- 2) 71. y =log5x2

8. 625 = 54

(,), 112. j = 2--7

9, 1 = i0-1

13. 10-2 = 0.01

16. log8 8

20. log5 (-25)

24, log I0,000

76, y = log5 x

79, y = 1 + logx

82, y = logs .v .... 2

77, y =31ogx

80. y - tog(x ..... 2) + I

183. y = log2 x +

Find the domain and the range of each functiom

Graph each logarithmic function.

73. v = log2x 74. y = 2!og2x

17. log4 8

21. log3 9

25, log5 !25

37. y = logsx

41).y = log3(x- 5) + 3

55. log7 16,807 = 5

1 -258. log3 ÿ =

61. log2 8192 = 13

66, 3' -- logl0 x

69. v = log 10x

72. y- loga(x- b)

75. y = log4 (2x + 3)

78. y= log2(x- 3)

81. y = log6 (x + 1)

84. y-- log (x t)

13