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Math Help - Can this problem be solved? (Natural Log)

  1. #1
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    Can this problem be solved? (Natural Log)

    I have this equation that needs to be solved for 'r'
    2*pi*a = e^(-2r) * (2r+1)
    The variable a is a constant but I need to solve for r in terms of a. I was going to take the natural log of both sides to eliminate the exponential, but that will end up putting the other r inside of a natural log function.
    Is there a way to solve for 'r' in terms of 'a' here?
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  2. #2
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    Is this your function?

    \displaystyle2\pi a = e^{(-2r) (2r+1)}

    or is it

    \displaystyle2\pi a = e^{-2r }(2r+1)
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  3. #3
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    The second one, sorry.
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  4. #4
    Master Of Puppets
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    I don't see a way.
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  5. #5
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    Thanks. I didnt either.
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  6. #6
    A Plied Mathematician
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    There are two special solutions, plus the product logarithm function solution. See here.
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