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Properties of Logarithms

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.

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Properties of Logarithms

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  1. Properties of Logarithms Change of Base Formula:

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

  3. Section 4.5 Properties of Logarithms Condense and Expand Logarithmic Expressions.

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

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

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

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

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

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

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

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

  12. 4. Expand the following expressions completely

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

  14. More practice….

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

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