Hi, I have an equation, x*e^x 1

[aj_k]

Hi,

I have an equation,
x*e^x = c(constant value)
How to calculate the value for x?
In the internet it says it is based up on Wlfraom equation.
And x= W(c)
But how to solve it?
Does any one know?

 

[IRstuff]

https://en.wikipedia.org/wiki/Lambert_W_function

Otherwise, use Excel, Mathcad, or SMath Studio to numerically solve for x

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[aj_k]

Thank you for your reaction.

FRom the wikipedia link, i have tried to solve it, but i am not getting the actual valuea.
Do you know how to do it in excel?
It will be really helpfull for me.

 

[IRstuff]

https://www.excel-easy.com/data-analysis/solver.html

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[BridgeSmith]

Do you know how to do it in excel?

Enter values for x in column A, starting in cell A1. In Cell B1, enter "=A1*EXP(A1)". Copy formula down Column B to get values of c for a given x.

If you want to get a specific x value for a given value of c, use Goal Seek (under the "Data" tab, click "What if Analysis" and choose "Goal Seek") to "Set cell" in Column B (c values) "To value" that you want for c, and choose the cell with the corresponding x value for the "By changing cell" box. Click "OK".

Edit: For something you can easily use over and over, without having to create a macro, the approach in IRStuff's link is probably the more useful way to handle it.

Rod Smith, P.E., The artist formerly known as HotRod10

 

[HTURKAK]

x*e^x = C
C is arbitrary constant. I will assign a value for C in order to show the calculation procedure.

Choose C= e^5 for simplicity . ( e is base of natural log = 2.718281828459 ) rewrite the equation=


x*e^x = e^5 know take the natural log of both sides:

ln X + Xln e = 5 ln e >
ln X+ X= 5 . Now define function f = ln X+ X -5 the value of X making f=0 is the solution of this nonlinear function . By inspection, the function is continuous (take derivative and see)

now give values for X ...By inspection for X = 4 f=0.386
for X=3 f=-0,901 > we can say that X shall be between 3 and 4

try average of them X= 3.5 f=-0.24723 > X must be between 3.5 and 4.
try average of them X= 3.75 f=0.072 > X must be between 3.5 and 3.75
try average of them X= 3.625 f=-0.0871 > X must be between 3.75 and 3.625
try average of them X= 3.6875 f=-0.00755 > so X =3.68 is accurate enough.. now try X=3.68 for the initial function > 3.68*e^3.68= e^5 left side =145.89 right side e^5=148.41 .

 

[IRstuff]

You do realize that Excel's solver is designed to do that directly?

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[r13]

I like HTURKAK's solve better, math is fun, if we still remember it. Computer does not stimulate the brain, and learn the process.

 

[BridgeSmith]

You do realize that Excel's solver is designed to do that directly?

I didn't until I read the link you posted. I might have to try it out sometime.

Rod Smith, P.E., The artist formerly known as HotRod10

 

[IRstuff]

"Computer does not stimulate the brain, and learn the process."

By that reasoning, we should be doing everything on slide rules ;-)

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[r13]

IR,

 

[IRstuff]

Well, I have used a slide rule, but a calculator was much faster and more accurate and eventually, programmable. That was the slippery slope and it's been all downhill from there.

Of course, there's no way in anywhere that you can even being to use a slide rule to do image processing calculations. Besides, we need to be standing on the shoulders of giants, so bring on the computing machines...

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[r13]

By doing math, we develop logic thinking, and learn how to solve problems through the process. Although by programming computer to solve math problem, we do need to know the basic to start with, but the process is largely kept in the black box. Computer is definitely essential in today's engineering, but OP's problem is rather too simple a task, if we remember how to solve it as demonstrated.

 

[aj_k]

Thank you so much for your help.

 

[HTURKAK]

You do realize that Excel's solver is designed to do that directly?

I didn't know until I read the link you posted. I installed yesterday and will try .
However, i prefer to prepare my own excell program rather than prepared by other..

 

[STrctPono]

I heard a quote once, I believe it was a modified Yogi Bhajan quote, probably by some software engineers...

If you want to learn something.... do it.
If you want to understand something..... teach it.
If you want to master something...... program it.

I believe there is some truth to that.

 

[IRstuff]

The issue with hand coding is that unless you can cleanly reuse previously vetted code, there's always a likelihood of coding errors.

We see this all the time in even "simple" Excel spreadsheets where the owner referenced an incorrect cell and got a plausible numerical answer, so didn't bother doing a thorough check. As it turned out, there was a mistake, and we had to fess up to the customer that we weren't meeting their spec.

Additionally, we potentially spend hours trying to debug our code, rather than doing ostensibly more productive work.

TTFN (ta ta for now)
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