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Math Help - express my equation as p=p(r)

  1. #1
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    express my equation as p=p(r)

    hi fellas, i need a very silly help for my work. i have this equation as r=r(p)

    r=p+0.645*(4*pi)^(-3/4)*p^(3/4)

    or, simply r=p+ap^(3/4), where a is a constant..
    what i need is an expression of my equation as p=p(r)..
    i want this whole term in respect of p now, this might be very silly but i don't get the exact curve in the graph when i m putting it using some logarithmic result.. i deduced it to be
    log p+(3/4)log p=log r-(3/4)log a.................and it might not be correct..
    can you please help me ?
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  2. #2
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    Re: express my equation as p=p(r)

    So hang on, is this your equation? $\displaystyle \begin{align*} r = p + 0.645 \left( 4\pi \right) ^{-\frac{3}{4}} p^{\frac{3}{4}} \end{align*}$?
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    Re: express my equation as p=p(r)

    yes exactly....now please tell me how to write is as a function of p=p(r)
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    Re: express my equation as p=p(r)

    Then that is not an exponential so taking logarithms will not help. I would let x= p^{1/4} so the equation becomes r= x^4+ .064(4\pi)^{-3/4}x^3 or x^4+ \left(0.54(4\pi)^{-3/4}\right)x^3- r= 0, a fourth degree polynomial equation.
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  5. #5
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    Re: express my equation as p=p(r)

    well, but how can i get only x on the left side of the equation? i have to express x=..........with only r and a on e right side
    anyway thanks for trying to help
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    Re: express my equation as p=p(r)

    Quote Originally Posted by cooper607 View Post
    well, but how can i get only x on the left side of the equation? i have to express x=..........with only r and a on e right side
    anyway thanks for trying to help
    the answer is a mess. There are 4 solutions.

    Solve[r == p + 0.645 (4 \[Pi])^(-3/4) p^(3/4), p] - Wolfram|Alpha
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  7. #7
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    Re: express my equation as p=p(r)

    thanks a lot
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