Properties of Logarithms Change of Base Formula:.

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Presentation transcript:

Properties of Logarithms Change of Base Formula:

The inverse function of an Exponential functions is a log function. The inverse function of an Exponential functions is a log function. Domain: Range: Key Points: Asymptotes: Graphing Logarithmic Functions

Section 4.5 Properties of Logarithms Condense and Expand Logarithmic Expressions.

Rewrite expression to get same base on each side of equal sign. where u and v are expressions in x where u and v are expressions in x Type 1. Solving Exponential Equations

Exponential Equations with base e Treat as a number. Rewrite these expressions to have a single base e on both sides of the equation

Type 2 Log = Log Type 2 Solving: Log = Log If then u = v When solving log functions, we must check that a solution lies in the domain!

Log ( ) = Constant Type 3. Solving: Log ( ) = Constant Isolate and rewrite as exponential

Exponential = Constant Type 4: Exponential = Constant Isolate exponential part and rewrite as log

1. Power Rule “Expanding a logarithmic expression” Rewrite using the power rule. “Expanding a logarithmic expression” Rewrite using the power rule.

2. Product Rule “Expanding a logarithmic expression” Rewrite using the Product Rule. “Expanding a logarithmic expression” Rewrite using the Product Rule.

3. Quotient Rule “Expanding a logarithmic expression” Rewrite using the Quotient Rule. “Expanding a logarithmic expression” Rewrite using the Quotient Rule.

4. Expand the following expressions completely

5. Condensing Logarithmic Expressions Rewrite as a single log expression Coefficients of logarithms must be 1 before you can condense them.

More practice….

7. Change-of-Base Formula Example. Find an approximation for