Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 decade ago

quick math question; exponenets?

(Pf) x (Vf)^x = (Pi) x (Vi)^x

I need to solve for Vi

I came up with

Vi = ((Pf) + ( Vf^x) - (Pi)) / (e^x)

can anyone confirm?

2 Answers

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  • 1 decade ago
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    Take the log of both sides of the equation, separate out (Vi), then exponentiate:

    (Pf) (Vf)^x = (Pi) (Vi)^x

    log(Pf) + xlog(Vf) = log(Pi) + xlog(Vi)

    xlog(Vi) = log(Pf) + xlog(Vf) - log(Pi)

    log(Vi) = (log(Pf) + xlog(Vf) - log(Pi))/x

    (Vi) = exp[(log(Pf) + xlog(Vf) - log(Pi))/x]

    (Vi) = [(Pf) + (Vf)^x - (Pi)]/(e^x)

    Yep.

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  • 1 decade ago

    p cancels as does v^x:

    f^(x+1)=i^(x+1) so f=i....

    its an identity so how cn u singl out Vi???

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