Download 3.3: Properties of Logarithms

10/27/2014
3.3: Properties of
Logarithms
College Algebra/Pre-Calculus
“I can . . .”
Use the product rule.”
Use the quotient rule.”
Use the power rule.”
Expand logarithmic expressions.”
Condense logarithmic expressions.”
Use the change-of-base property.”
Product Rule:
• Let b, M, and N be positive real numbers with
b ≠ 1.
= + • Ex. 1: Expand the logarithmic expression.
( ∙ ) →
() →
1
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Quotient Rule:
• Let b, M, and N be positive real numbers with
b ≠ 1.
• Ex. 2: Expand the logarithmic expression.
( ) →
( ) →
Power Rule:
• Let b and M be posiƟve real numbers with b ≠
1, and let p be any real number.
= • Ex. 3: Expand the logarithmic expression.
→
→
( + ) →
2
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Expanding Logarithmic
Expressions:
Ex. 4: Use properties to expand each expression as much as
possible. Where possible, evaluate logarithmic expressions
without the using a calculator.
a) (
)
b) (
)
Expanding Logarithmic
Expressions:
Ex. 4: Use properties to expand each expression as much as
possible. Where possible, evaluate logarithmic expressions without
the using a calculator.
]
c) [
d) 3
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Condensing Logarithmic
Expressions:
Ex. 5: Use properties to condense each expression. Write the
expression as a single logarithm whose coefficient is 1. Where
possible, evaluate logarithmic expressions without the using a
calculator.
a) ! + − !
b) + Condensing Logarithmic
Expressions:
Ex. 5: Use properties to condense each expression. Write the expression
as a single logarithm whose coefficient is 1. Where possible, evaluate
logarithmic expressions without the using a calculator.
c) + + d)
−
− 4
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Change of Base Property:
Common Logarithms:
= Natural Logarithms:
= # # Change of Base:
Ex. 6: Use common logarithms or natural logarithms
to evaluate to four decimal places.
a) b) $ 5
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3.3 Properties of Logarithms
Practice Problems:
Page 449: 3-78
mult. of 3
Timeline:
• Fri. (10/31):
• 3.2 Quiz
• 3.5 Notes
• Tues. (11/4):
• 3.3 Quiz
• 3.4 Notes
• Thurs. (11/6):
• 3.5 Quiz
• 4.1 Notes
• Mon. (11/10):
• 3.4 Quiz
• 4.2 Notes
• Wed. (11/12):
• CHAPTER 3 TEST
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