8.5 Properties of Logarithms

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8.5 Properties of Logarithms

• p. 493
• What are the three properties of logs?
• How do you expand a log? Why?
• How do you condense a log?

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Properties of Logarithms

• Let b, u, and v be positive numbers such that
  b?1.
• Product property
• logbuv logbu logbv
• Quotient property
• logbu/v logbu logbv
• Power property
• logbun n logbu

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Use log53.683 and log571.209

• Approximate
• log53/7
• log53 log57
• .683 1.209
• -.526

• log521
• log5(37)
• log53 log57
• .683 1.209
• 1.892

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Use log53.683 and log571.209

• Approximate
• log549
• log572
• 2 log57
• 2(1.209)
• 2.418

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Expanding Logarithms

• You can use the properties to expand logarithms.
• log2
• log27x3 - log2y
• log27 log2x3 log2y
• log27 3log2x log2y

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Your turn!

• Expand
• log 5mn
• log 5 log m log n
• Expand
• log58x3
• log58 3log5x

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Condensing Logarithms

• log 6 2 log2 log 3
• log 6 log 22 log 3
• log (622) log 3
• log
• log 8

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• What are the three properties of logs?
• Productexpanded add each, Quotientexpand
  subtract, Powerexpanded goes in front of log.
• How do you expand a log? Why?
• Use logb before each addition or subtraction
  change. Power property will bring down exponents
  so you can solve for variables.
• How do you condense a log?
• Change any addition to multiplication,
  subtraction to division and multiplication to
  power. Use one logb

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Assignment

• p. 496
• 15-55 odd
• Skip 29

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Properties of LogarithmsDay 2

• What is the change of base formula?
• What is its purpose?

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Your turn again!

• Condense
• log57 3log5t
• log57t3
• Condense
• 3log2x (log24 log2y)
• log2

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Change of base formula

• u, b, and c are positive numbers with b?1 and
  c?1. Then
• logcu
• logcu (base 10)
• logcu (base e)

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Examples

• Use the change of base to evaluate
• log37
• (base 10)
• log 7
• log 3
• 1.771

• (base e)
• ln 7
• ln 3
• 1.771

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What is the change of base formula? What is
its purpose? Lets you change on base other than
10 or e to common or natural log.
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Assignment

• Page 496,
• 30-56 even,
• 59-73 odd