# Thread: rearrange tough equation

1. ## 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)))

2. ## 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*}?

3. ## Re: rearrange tough equation

hi, yes that is the correct equation. thanks for that.

4. ## 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?

5. ## Re: rearrange tough equation

Thanks for your reply. It is a fitted surface equation. Can the Lambert W function be used at all?

6. ## 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.

7. ## Re: rearrange tough equation

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

8. ## 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.

9. ## Re: rearrange tough equation

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?

10. ## 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 $F=10^{a+b}$

$A=F10^{e^V}$

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

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

$log_e(log_{10}\frac{A}{F})=V$

11. ## Re: rearrange tough equation

After your substitution, you would have instead:

$A=10^{b^V+a^V}$

12. ## Re: rearrange tough equation

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

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

13. ## Re: rearrange tough equation

Originally Posted by dave2014
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.