# Thread: express my equation as p=p(r)

1. ## 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..

2. ## 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*}?

3. ## 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)

4. ## 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.

5. ## 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

6. ## Re: express my equation as p=p(r)

Originally Posted by cooper607
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

thanks a lot