HELP to solve an exponential equation with one unknown

[LanieH]

Hi,
I have an equation with one unknown. This is the 'B' in the equation. I need to solve for 'B'. Can you help me to rearrange this complex equation to solve for B in terms of everything else please?

=(() - (DCRMgAl)) ∗ ^(−∗(()+()))+ ((DCRMgAl )- (DCRAl ))∗ ^(−∗∗() )+((Al) - (DCRMg)) ∗ ^(−∗(()+()))

 

[Simon Bridge]

��=((����������) - (DCRMgAl)) ∗ ��^(−��∗((������)+(������)))+ ((DCRMgAl )- (DCRAl ))∗ ��^(−��∗��∗(������) )+((������Al) - (DCRMg)) ∗ ��^(−��∗((������)+(����������)))

... well it's perfectly simple, all you have to do is put � = �_(−��) and then it should all be clear :D

 

[LanieH]

0=((DCRMg) - (DCRMgAl)) ∗ e^(-B∗((ρMg)+(ρAl)))+ ((DCRMgAl )- (DCRAl ))∗e^(-2∗B∗(ρMg))+((DCRAl) - (DCRMg)) ∗e^(-B∗((ρMg)+(ρMgAl)))

Haha :-) I hope that I can enter the equation correctly this time...

 

[Ray Vickson]

0=((DCRMg) - (DCRMgAl)) ∗ e^(-B∗((ρMg)+(ρAl)))+ ((DCRMgAl )- (DCRAl ))∗e^(-2∗B∗(ρMg))+((DCRAl) - (DCRMg)) ∗e^(-B∗((ρMg)+(ρMgAl)))

Haha :-) I hope that I can enter the equation correctly this time...

It looks like you have an equation of the form
$$a_1 e^{-b_1 B} + a_2 e^{-b_2 B} + a_3 e^{-b_3 B} = 0,$$
where
$$a_1 = DCRMg - DCRMgAl, \, a_2 = DCRMgAl - DCRAl, \, a_3 = DCRAl - DCRMg\\ b_1 = \rho Mg + \rho Al, \, b_2 = 2 \rho Mg, \, b_3 = \rho Mg + \rho MgAl.$$
Is that correct? If so, you had better have mixed signs for a₁, a₂ and a₃, because if they all have the same sign there cannot be any real solution. If they DO have mixed signs, just use a standard numerical equation-solving method, or use a computer package such as Wolfram Alpha, or the EXCEL Solver.

RGV

 

[LanieH]

Thank you for your help. I have been recently told that this equation must be solved using Excel Solver. I have no idea how to use this program in order to calculate B.
I have created an excel formula relative to the above equation, but I am stuck at this point. Are you able to show me how you would solve the equation for B in Excel Solver?

=(B50-C50)*EXP(-B*($H$44+$I$44))+(C50-D50)*EXP((-2*B($H$44)))+(D50-B50)*EXP((-B($H$44+$J$44)))

 

[Simon Bridge]

Oh I hate courses like that - it is as if the teacher is a Microsoft sales rep.
(I'm guessing the Mg and Al stuff are subscripts? So $\rho_{Mg}$ would be the density of magnesium?)

FWIW since I too have no experience nor interest in Excel.
How would the marker know you didn't use a different approach to solve it?
Say - Newton-Raphson in gnu-octave or something?

 

[LanieH]

This is a formula used in an Australian Standard. I need to validate it in Excel Solver to prove that a piece of calibrated equipment is providing me with close to accurate results. Since I cannot solve the equation on paper, I require a program to do it for me. This is where Solver was suggested to me.

 

[Ray Vickson]

This is a formula used in an Australian Standard. I need to validate it in Excel Solver to prove that a piece of calibrated equipment is providing me with close to accurate results. Since I cannot solve the equation on paper, I require a program to do it for me. This is where Solver was suggested to me.

If the EXCEL Solver is all you have access to, then go ahead and use it. However, there are much better, much more accurate solvers available. Did you miss my suggestion to use Wolfram Alpha?

Actually, the type of problem you have could easily be done manually, using nothing fancier than a scientific hand-held calculator and Newton's method. Your results obtained in this way might well be more accurate than those from the EXCEL Solver!

RGV

 

[Simon Bridge]

Yeah, why should the equipment need to be validated with excel in particular and not any other bit of software?
(Maybe the firm has a deal with Microsoft?)

I'm used to doing this the other way around - since - for scientific transparency it is good practice that all parts of the software used in a calculation be open, in principle at least, to scrutiny. That pretty much means open source. So I tend to end up validating results from closed source tools using open source or even just writing my own program and using an open-source compiler.

However - not to be a total killjoy, if solver you must use then solver it is.
There are plenty of references and tutorials online -eg:
http://www.solver.com/excel-solver-help

 

[Ray Vickson]

This is a formula used in an Australian Standard. I need to validate it in Excel Solver to prove that a piece of calibrated equipment is providing me with close to accurate results. Since I cannot solve the equation on paper, I require a program to do it for me. This is where Solver was suggested to me.

I don't understand what your requirements are. I understand that you have some equipment that needs to be checked or calibrated. To do that, you need to solve some equation and then do something with the solution. Have I got that correct so far?

At this point you lose me completely: why should it matter what method you use to obtain the solution? Suppose you e-mailed me all the numerical values of the input parameters and I e-mailed you back the numerical solution of the problem (which you could easily check just by substitution). Would that not be all you need? Are you being forced to do it in EXCEL?

RGV