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**Properties of Logarithmic Functions**

Objective: Simplify and evaluate expressions involving logarithms.

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**Product and Quotient Properties of Logarithms**

For Product Property

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**Product and Quotient Properties of Logarithms**

For Product Property Quotient Property

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**Product and Quotient Properties of Logarithms**

For Product Property Quotient Property You can use these properties to evaluate logarithmic expressions.

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Example 1

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Example 1

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Example 1

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Try This Given that , approximate each expression.

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Try This Given that , approximate each expression.

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Try This Given that , approximate each expression.

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Example 2

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Example 2

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Example 2

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Try This Write each expression as a single logarithm. Then, simplify if possible.

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Try This Write each expression as a single logarithm. Then, simplify if possible.

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Try This Write each expression as a single logarithm. Then, simplify if possible.

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**The Power Property of Logarithms**

For , and any real number p:

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Example 3

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Example 3

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Try This Evaluate

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Try This Evaluate

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**Exponential-Logarithmic Inverse Properties**

For b > 0 and :

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Example 4

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Example 4

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Example 4

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Try This Evaluate each expression.

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Try This Evaluate each expression.

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Try This Evaluate each expression.

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**One-to-One Property of Logarithms**

If , then x = y.

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Example 5

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Example 5

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Example 5

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Homework Page 382 13-61 odd

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Properties of Logarithms Section 6.5 Beginning on page 327.

Properties of Logarithms Section 6.5 Beginning on page 327.

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