Properties of Logarithms

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Properties of Logarithms

• Today you will use the properties of logarithms
  to simplify expressions.

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Like Mr. Carnes, you too may someday enjoy the
luxuries that the world of mathematics can bring!
Nowfor some log fun!
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Properties of Logarithms
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Product Property
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Quotient Property
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Powering Property
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Use the Properties of Logarithms to expand each
expression.
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Use the Properties of Logarithms to condense each
expression.
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Solve each expression.
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Solving Equations

• When solving equations where the variable is in
  the exponent...we use logarithms because if we
  take the log of both sides then we can use the
  powering property to bring the variable out of
  the exponent.
• We use the common and natural logs to solve
  because those are the values that are programmed
  into our calculators.

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Solve the equation by writing as an exponent then
take the log of both sides.
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Change of Base Theorem
This is just a shortcut, if you take the log of
both sides and apply the powering property, you
end up with the same result.
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Write the expression using only natural
logarithms. (same as setting equation to y and
solving using the properties.)
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Write the expression using only common logarithms
(same as setting equation to y and solving
using the properties).
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Assignment

• A 4.10 Sect III
• Pgs. 317-318
• 3, 7, 9, 14, 16, 22, 29, 30, 33, 34,
• 43-46, and 54