Logarithmic Functions

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Section 3.2

• Logarithmic Functions

2
The Logarithmic Function
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The Big Idea

• The logarithmic function is the inverse of the
  exponential function.

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Important Equivalency

• Is equivalent to

5
Convert From Logarithmic to Exponential
6
Convert from Exponential to Logarithmic
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How to Find Logs

1. Use what you know. If you know that 2 to the 3rd
   power is 8, then you also know that the log, base
   2, of 8 is 3.
2. Use properties of exponents and radicals. Taking
   the square root of something is the same as
   raising that same thing to the ½ power. And
   fractions can often be re-written using negative
   exponents.

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Evaluate the Following Log Expressions
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How to Find Logs, continued

• 3. Use these helpful log properties

10
Evaluate the Following Log Expressions
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The domain of a logarithmic function

• It is not possible to take the log of a negative
  number.
• To find the domain of a logarithmic function, set
  the argument gt 0.

12
Find the domain of each logarithmic function
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Natural and Common Logs

• Logs to the base of 10 are called common logs
  (log on your calculator)
• Logs to the base of e are called natural logs (ln
  on your calculator)

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Evaluate the Following Log Expressions
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Graphs of Logarithmic Functions

• You may omit questions dealing with graphs on
  both the homework (15 18) and the quiz (6 and
  7). I will give you credit for those questions.