More Properties of Logarithms

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Presentation transcript:

More Properties of Logarithms Section 11.6 More Properties of Logarithms

Product Property for Logarithms Product Property of Logarithms Property For In words: The sum of logarithms is the logarithm of the product of their inputs. Simplify and write as a sum of logarithms as a single logarithm. Example

Product Property for Logarithms Using the Product Property for Logarithms Solution

Quotient Property for Logarithms Quotient Property of Logarithms Property For In words: The difference of logarithms is the logarithm of the quotient of their inputs.

Simplify and write as a single logarithms with coefficient of 1. Quotient Property for Logarithms Quotient Property of Logarithms Example Simplify and write as a single logarithms with coefficient of 1. Solution

Product Property for Logarithms Product and Quotient Properties Solution Continued Solution

Product Property for Logarithms Product and Quotient Properties Solution Continued

Solving Logarithmic Equation Solving a Logarithmic Equation Example Solve Solution

Solving Logarithmic Equation Solving a Logarithmic Equation Solution Continued There is a negative root of 125/144 The original equation contains 4log5(2x) Domain of logarithms must be positive Hence, x must be positive

Solving Logarithmic Equation Solving a Logarithmic Equation Example Solve Solution

Solving Logarithmic Equation Solving a Logarithmic Equation Solution Continued

Change-of-Base Property For Find Use the change-of-base property to write log2(12) in terms of base 10 Example Solution

Use the log key on the calculator to compute Change-of-Base Property Converting to log10 Property Solution Continued Use the log key on the calculator to compute

Change-of-Base Property Using Change-of-Base Property Example Write as a single logarithm. Use the change-of-base property Use a graphing calculator to graph Solution Example

Use the change-of-base property Using a Graphing Calculator to Solve an Equation in One Variable Solution Use the change-of-base property

Comparing Properties of Logarithms Common Error Warning