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A28-4 log fxns

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Transcript

  • 1. Logarithmic Functions
    Algebra 2
    8.4
  • 2. Logarithmic Functions
    2x = 6
    You know that 22< 6 < 23, so that means
    2 < x < 3.
  • 3. Mathematicians use logarithms to find the exact value of exponents like this example.
  • 4. 2x = 6 can also be written in log form:
    log2 6 = x
  • 5. 2x = 6 can also be written in log form:
    log2 6 = x
    Exponential form
    Logarithmic form
  • 6. Log Functions
    Log functions are inverses of exponential functions.
  • 7. The graphs of inverse functions are symmetric across the line
    y = x.
  • 8. The Domain and Range for exponential functions are opposite for log functions.
  • 9. Graphing Log Functions
    The line x = h is a vertical asymptote.
  • 10. Graphing Log Functions
    The line x = h is a vertical asymptote.
    If b > 1, the graph is increasing.
  • 11. y = logb (x – h) + k
    Graphing Log Functions
    The line x = h is a vertical asymptote.
    If b > 1, the graph is increasing.
    If 0 > b > 1, the graph is decreasing.