7.3 Logarithmic Functions as Inverses

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7.3 Logarithmic Functions as Inverses
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• Def Logarithm
• The logarithm to the base b of a positive number
  y is defined
• If y bx, then logb y x

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• Example
• Write 729 36 and (1/2)3 1/8 in log form.
• 729 36 can be written as
• log3 729 6
• and (1/2)3 1/8 written as
• log(1/2) (1/8) 3

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• Evaluating Logs
• Ex. Evaluate log9 27. What number must you raise
  9 too, to get 27?
• So 9x 27
• 32x 33
• so 2x 3 or x 3/2

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• Def
• A common logarithm is a logarithm that uses base
  10. You can write the common log as log10 or just
  log.
• log log10

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• Graphing log functions.
• A log function is the inverse of an exponential
  function. We graph inverses over the line yx.

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• The domain of the log is x gt 0. 
• The range is all real numbers. 
• The zero is at x 1. 
• You can only find the log of positive numbers. 
• Logs of numbers less than one are negative and
  logs of numbers greater than one are positive.
• We can translate log functions just like any
  other function we already seen.

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• Hw pg 456 12 31 all, 40-43 all