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COMMON and Natural Logarithms.

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Presentation on theme: "COMMON and Natural Logarithms."— Presentation transcript:

1 COMMON and Natural Logarithms

2 COMMON LOGARITHMS

3 Mathematicians know that the base is understood to be 10
When you see Mathematicians know that the base is understood to be

4 COMMON LOGARITHMS

5 Definition

6 Definition

7

8

9

10

11

12

13

14 Exponent # Zeros

15

16

17 ?

18 Powers of 10

19 One Tenth

20

21

22 One Hundredth

23

24

25

26 One Thousandth

27

28

29

30 One Millionth

31 # Decimal Places # Zeros

32 # Exponent # Decimal Zeros Places

33 # Exponent # Decimal Zeros Places

34 Back To Logarithms

35

36

37

38

39

40

41

42

43

44 # Decimal Places

45 # Decimal Places

46

47

48 Students who went to school before 1960 had to use
Logarithm Tables

49 Using a partial section of the table
for example Using a partial section of the table

50 Scientific Notation

51 Digits

52 200

53 200

54

55 Today

56 Natural Logarithms

57 New Base The Natural Number

58 Used in formulas about population growth
Used in formulas about continuous interest Used in formulas about gravity Used in CALCULUS

59

60 like Irrational

61 Abbreviation

62 Therefore They Are Equivalent

63 Write In Exponential Form

64 Definition

65 Definition

66 Definition

67 Definition

68 Definition

69 Definition

70 Next Example

71 Definition

72 Definition

73 Definition

74 Definition

75 Definition

76 Definition

77 Next Example

78 Definition

79 Definition

80 Definition True

81 Exponential to Logarithm

82 Definition How Do We Appreviate

83 Definition

84 Definition

85 Definition

86 Definition

87 Definition

88 Next Example

89 Definition

90 Definition

91 Simplify

92 Definition

93 Definition

94 Definition

95 Definition

96 Definition

97 Definition Simplifed

98 Next Example

99 Definition

100 Definition

101 Definition Simplifed

102 You Try

103 Definition Simplifed

104 Solve Equations

105 Definition Solve for x

106 Definition

107 Definition

108 Definition

109 Definition Solution

110 You Try

111 Definition Solution

112 Next Example

113 ? Law 1

114 Same Log Base

115 N's are equal

116 You Solve

117 But Recall

118 Restrictions on b

119 x

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