# rearrange tough equation

• April 30th 2013, 04:18 AM
dave2014
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)))
• April 30th 2013, 04:35 AM
Prove It
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*}?
• April 30th 2013, 04:52 AM
dave2014
Re: rearrange tough equation
hi, yes that is the correct equation. thanks for that.
• April 30th 2013, 05:22 AM
Prove It
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?
• April 30th 2013, 07:06 AM
dave2014
Re: rearrange tough equation
Thanks for your reply. It is a fitted surface equation. Can the Lambert W function be used at all?
• May 9th 2013, 05:54 AM
dave2014
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.
• May 9th 2013, 05:45 PM
topsquark
Re: rearrange tough equation
Quote:

Originally Posted by dave2014
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
• May 9th 2013, 08:16 PM
ibdutt
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.
• May 10th 2013, 12:44 AM
dave2014
Re: rearrange tough equation
Quote:

Originally Posted by topsquark
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?
• May 10th 2013, 03:07 AM
Shakarri
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 $F=10^{a+b}$

$A=F10^{e^V}$

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

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

$log_e(log_{10}\frac{A}{F})=V$
• May 10th 2013, 03:29 AM
MarkFL
Re: rearrange tough equation

$A=10^{b^V+a^V}$
• May 10th 2013, 05:43 AM
Shakarri
Re: rearrange tough equation
Quote:

Originally Posted by MarkFL
$A=10^{b^V+a^V}$