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Math Help - rearrange tough equation

  1. #1
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    Question rearrange tough equation

    Hi, I am trying to rearrange the following equation to isolate V, but am having trouble working out the right strategy. Could someone help me by pointing me in the right direction? I have read about the Lambert W function and it seems like it might be suitable but don't know how to use it. Thanks a lot.

    Rearrange to isolate V:

    A = 10^(K*(e^(c_1*V))+(e^(c_2*V)))
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  2. #2
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    Re: rearrange tough equation

    It might help to read this LaTeXed, is your equation \displaystyle \begin{align*} A = 10^{K\,e^{c_1V} + e^{c_2V}} \end{align*}?
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    Re: rearrange tough equation

    hi, yes that is the correct equation. thanks for that.
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    Re: rearrange tough equation

    I don't think it's possible to isolate V in this case. Can you tell us where this problem came from please?
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    Re: rearrange tough equation

    Thanks for your reply. It is a fitted surface equation. Can the Lambert W function be used at all?
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  6. #6
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    Re: rearrange tough equation

    Hi, could someone provide some more guidance on this problem please? If it is impossible to rearrange, then what approach can I take to solve it? thanks again.
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    Re: rearrange tough equation

    Quote Originally Posted by dave2014 View Post
    Hi, could someone provide some more guidance on this problem please? If it is impossible to rearrange, then what approach can I take to solve it? thanks again.
    Lambert isn't going to help here. I know of no way to solve for V. If you had some numbers for the other variables then you might be able to do it numerically.

    -Dan
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    Re: rearrange tough equation

    Please indicate as what have you done so far. I feel there is something missing in the question. I don't think we can isolate V in its present form.
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    Re: rearrange tough equation

    Quote Originally Posted by topsquark View Post
    Lambert isn't going to help here. I know of no way to solve for V. If you had some numbers for the other variables then you might be able to do it numerically.

    -Dan
    Hi Dan, thanks for your reply. I have the values for c1 and c2 only, not K or V. Does that help at all?
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    Re: rearrange tough equation

    People are saying this is impossible so maybe I'm missreading it but here's my attempt

    \displaystyle \begin{align*} A = 10^{K\,e^{c_1V} + e^{c_2V}} \end{align*}

    Let b=Ke^{c_1}, a=e^{c_2}

    A=10^{be^V+ae^V}

    A=10^{(b+a)e^V}

    Let F=10^{a+b}

    A=F10^{e^V}

    \frac{A}{F}=10^{e^V}

    log_{10}\frac{A}{F}=e^V

    log_e(log_{10}\frac{A}{F})=V
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  11. #11
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    Re: rearrange tough equation

    After your substitution, you would have instead:

    A=10^{b^V+a^V}
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    Re: rearrange tough equation

    Quote Originally Posted by MarkFL View Post
    After your substitution, you would have instead:

    A=10^{b^V+a^V}
    Ah you're right. Thanks, I'm mixing up indices rules.
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    Re: rearrange tough equation

    Quote Originally Posted by dave2014 View Post
    Hi Dan, thanks for your reply. I have the values for c1 and c2 only, not K or V. Does that help at all?
    Actually I also know values for K and A, it is just V I do not know. Thanks everyone for your efforts so far, does knowing K, A, c1, and c2 help at all? Thanks.
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