Properties of Logarithms

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Properties of Logarithms. Change of Base Formula:. Graphing Logarithmic Functions. The inverse function of an Exponential functions is a log function. Domain: Range: Key Points: Asymptotes:. Section 4.5 Properties of Logarithms. Condense and Expand Logarithmic Expressions. - PowerPoint PPT Presentation

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Slide 1

Properties of Logarithms

Change of Base Formula:1

The inverse function of an Exponential functionsis a log function.

Domain:Range:Key Points:Asymptotes: Graphing Logarithmic Functions

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Section 4.5Properties of LogarithmsCondense and Expand Logarithmic Expressions.

3Rewrite expression to get same base on each side of equal sign.

where u and v are expressions in x

Type 1. Solving Exponential Equations

4Exponential Equations with base eTreat as a number.

Rewrite these expressions to have a single base e on both sides of the equation5Type 2 Solving: Log = LogIf then u = v

When solving log functions, we must check that a solution lies in the domain!

6Type 3. Solving: Log ( ) = ConstantIsolate and rewrite as exponential

7Type 4: Exponential = ConstantIsolate exponential part and rewrite as log

81. Power RuleExpanding a logarithmic expressionRewrite using the power rule.

92. Product RuleExpanding a logarithmic expressionRewrite using the Product Rule.

103. Quotient RuleExpanding a logarithmic expressionRewrite using the Quotient Rule.

114. Expand the following expressions completely

125. Condensing Logarithmic ExpressionsRewrite as a single log expression

Coefficients of logarithms must be 1 before you can condense them.13

More practice.147. Change-of-Base Formula

Example.Find an approximation for

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