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Math Help - Notation of solution

  1. #1
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    Notation of solution

    ln(x)(sin(x)) = 0
    for x= 0, Pi, 2Pi etc... and for 1
    how do you write this correctly with the correct symbols and terms?
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  2. #2
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    Quote Originally Posted by Schdero View Post
    ln(x)(sin(x)) = 0
    for x= 0, Pi, 2Pi etc... and for 1
    how do you write this correctly with the correct symbols and terms?
    Write it as

    x = \left\{1, \pi n\right\}, where n \in \mathbf{Z}.
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  3. #3
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    Quote Originally Posted by Schdero View Post
    ln(x)(sin(x)) = 0
    for x= 0, Pi, 2Pi etc... and for 1
    how do you write this correctly with the correct symbols and terms?
    Notice that any value in the range x\le0 is actually not a solution because \ln x will be undefined in that region.

    So the solution should be
    1,~k\pi where k is a natural number
    or, if you want to be precise (this is not usually necessary unless you are in advanced math courses where you've learned set theory), you should use set notation, i.e.,
    x \in \{1\} \cup \{k\pi:k\in\mathbb{N}\}
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