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Properties of Logarithms Section 8.5

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WHAT YOU WILL LEARN: 1.How to use the properties of logarithms to simplify and evaluate expressions.

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Some Questions How do you simplify the following:

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So ….. Remember that logarithms are another way to write exponents. The Properties of Logarithms are based on the properties of exponents – Product Property: Quotient Property: Power Property:

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Using Properties of Logarithms Use to approximate the following: 1. 2. log 5 21 3. log 5 49

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You Try! Use to approximate the following: 1. 2. log 9 55 3. log 9 25

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Expanding a Logarithmic Expression Expand. Assume x and y are positive.

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You Try! Expand. Assume x and y are positive.

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Condensing a Logarithmic Expressions Condense log 6 + 2 log 2 – log 3

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You Try! Condense

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Change of Base Formula and

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Example Evaluate the expression log 3 7 using common and natural logarithms. 1. log 3 7 2. log 3 7

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Homework page 496, 14-24 even, 30-42 even, 46-52 even, 58, 60, 70

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8.5 Properties of Logarithms 3/21/2014. Properties of Logarithms Let m and n be positive numbers and b ≠ 1, Product Property Quotient Property Power Property.

8.5 Properties of Logarithms 3/21/2014. Properties of Logarithms Let m and n be positive numbers and b ≠ 1, Product Property Quotient Property Power Property.

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