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Math Help - Logarithmic function help

  1. #1
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    Logarithmic function help

    Dear all it have been many years since I stopped reading maths.

    Today I have tried to solve the following equation. K is the only unknown factor. So I tried to keep only K in the right part of the equation and put all the others to the left side. As I am not good in math notations in internet please accept my attached image

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    It seems that I luck some knowledge how to solve that.

    Could you please help me?

    Best Regards
    Alex
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  2. #2
    MHF Contributor

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    Your equation has "K" both inside a transcendental function, log(K), and outside it. Such equations cannot, in general be solved in terms of elementary functions. You might be able to solve for K in terms of "Lambert's W function" which is defined as the inverse function to f(x)= xe^x.
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  3. #3
    Junior Member
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    Quote Originally Posted by HallsofIvy View Post
    Your equation has "K" both inside a transcendental function, log(K), and outside it. Such equations cannot, in general be solved in terms of elementary functions. You might be able to solve for K in terms of "Lambert's W function" which is defined as the inverse function to f(x)= xe^x.
    Thanks a lot
    Could you please provide me moe information? What is that Lambert's W function and how can I try to solve it?

    Regards
    Alex
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