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Math Help - How to solve equation with many exp

  1. #1
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    How to solve equation with many exp

    Hi

    I'm trying to understand how to solve this type of equation and don't know.
    A*exp(x/B)+Cexp(x/D)+Fexp(x/G)+Kexp(x/L)+Mexp(x/N)=0

    I need to find x.

    Thanks for your help,
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  2. #2
    MHF Contributor
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    Welcome to the forum.

    If one of B, D, G, L, N is a multiple of the rest, then this problem reduces to finding roots of a polynomial. For example, suppose that B = d * D = g * G = l * L = n * N for some positive integer d, g, l, n. Then e^{x/D}=e^{(x/B)\cdot d}=(e^{x/B})^d. So, the equation becomes Ay+Cy^d+Fy^g+Ky^l+My^n=0 for y=e^{x/B}.

    Do you need to solve this equation symbolically or numerically? Is there some background knowledge that you need to use? Also, depending on these answers, you need to post this question to the right forum (this one is about discrete mathematics).
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  3. #3
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    Thank you, that is what I needed. I'll try to work it out
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