Logarithm of Negative Numbers

Discussion in 'Other Pre-University Math' started by nycmathguy, Oct 14, 2021.

  1. nycmathguy

    nycmathguy

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    Section 3.2

    20211013_083700.jpg

    Let f(x) = log x

    Let x = -2

    f(-2) = log (-2) = error

    Just like Ron Larson stated above, we cannot take the log of negative 2 "...because there is no real number power to which 10 can be raised to obtain -2.

    Question:

    Is there a complex number power to which 10 can be raised to obtain -2?
     
    Last edited: Oct 14, 2021
    nycmathguy, Oct 14, 2021
    #1
  2. nycmathguy

    MathLover1

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    log (-2) = log(2) + i *π
     
    MathLover1, Oct 14, 2021
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    nycmathguy likes this.
  3. nycmathguy

    nycmathguy

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    This is beyond precalculus. Yes?
     
    nycmathguy, Oct 14, 2021
    #3
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