# Properties of Logarithmic Functions

## Presentation on theme: "Properties of Logarithmic Functions"— Presentation transcript:

Properties of Logarithmic Functions
Objective: Simplify and evaluate expressions involving logarithms.

Product and Quotient Properties of Logarithms
For Product Property

Product and Quotient Properties of Logarithms
For Product Property Quotient Property

Product and Quotient Properties of Logarithms
For Product Property Quotient Property You can use these properties to evaluate logarithmic expressions.

Example 1

Example 1

Example 1

Try This Given that , approximate each expression.

Try This Given that , approximate each expression.

Try This Given that , approximate each expression.

Example 2

Example 2

Example 2

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

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

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

The Power Property of Logarithms
For , and any real number p:

Example 3

Example 3

Try This Evaluate

Try This Evaluate

Exponential-Logarithmic Inverse Properties
For b > 0 and :

Example 4

Example 4

Example 4

Try This Evaluate each expression.

Try This Evaluate each expression.

Try This Evaluate each expression.

One-to-One Property of Logarithms
If , then x = y.

Example 5

Example 5

Example 5

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