6.5 - Properties of Logarithms

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6.5 - Properties of Logarithms

• Objective TSW Apply the properties of
  logarithms.

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Properties of LogarithmsIf M, N, and b are
positive numbers and b?1, then

• Product Property
• log b MN log b M log b N
• Quotient Property
• log b M log b M - log b N
• N

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Properties of Logarithms

• Power Property log b Mp p log b M

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Examples Expand the following logarithms.

• 1. log b 2x
• y
• log b 2
• rs
• 3. log b x2 y3

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Now, condense the following logarithms into one
logarithmUse the properties backwards.
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Properties of Logarithmsb is a positive number
and b?1

• log b 1 0 since b0 1
• Example log 7 1
• log b b 1 , since b1 b
• Example log 7 7

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Properties of Logarithms

• log b bx x, since bx bx
• Example log 7 72
• blogbx x , since log b x is the exponent to
  which b is raised to get x
• Example 7log72
• 4log48

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Examples Simplify the following

• 6. log 9 1 log 2 8
• 7. log 8 83 - log 3 1/9
• 8. 6log64 log 4 64
• 9. log 6 6 - log 9 1

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Solve for x.
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pgs. 512-513 s 7-25(odds), 29-49(odds)