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Question about logarithmic differentiation

  1. Mar 8, 2015 #1
    I have a question about logarithmic differentiation, especially concerning the absolute value involved. For example, if we have the function ##y = 2^x \sin x##, the domain is all real numbers. So what happens when we take ##\ln## of both sides of the equation? The antilogarithm must be greater than ##0##, but the domain of the function is all real numbers. How do we account for this? I know the answer has something to do with absolute value, but I am not sure how...
     
  2. jcsd
  3. Mar 8, 2015 #2

    mathman

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    Science Advisor
    Gold Member

    Ln of negative numbers gets you into complex analysis. I suggest you make your question more specific.
     
  4. Mar 8, 2015 #3

    Mark44

    Staff: Mentor

    Assuming that you're concerned only with real-valued functions, since the domain of ln is positive reals, ##\ln(2^x\sin(x))## is defined only for intervals in which sin(x) > 0, open intervals of the form ##(2k\pi, (2k + 1)\pi)##, with k in the integers. For the other intervals, ##\ln(2^x\sin(x))## is not defined, resulting in gaps in the graph.
     
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