Solving 3((e^x)-1)-xe^x=0 Equation

[hamamo]

hi there;
please can anyone help me solving this
3((e^x)-1)-xe^x=0
sorry i couldn't use more elegant form to write the equation
i use some software and they help
but i can't do it in hand

 

[sutupidmath]

hi there;
please can anyone help me solving this
3((e^x)-1)-xe^x=0
sorry i couldn't use more elegant form to write the equation
i use some software and they help
but i can't do it in hand

3(e^{x}-1)-xe^{x}=0 I do not believe you can solve this one algebraically, one can only approximate the solution to these kind of equations.

 

[Marco_84]

i think a graphical method is usefull...

ciao

 

[hamamo]

thanx for the reply up there
but i search more and i found this kind of equation can be solved using
Lambart w-function
or omega function, the problem i couldn't have more information about this function else some expansion series and i can't even write a code to solve or to find a value in lambart function
any more help will be useful
thanx

 

[hamamo]

3(e^{x}-1)-xe^{x}=0 I do not believe you can solve this one algebraically, one can only approximate the solution to these kind of equations.

can you help me using the latex

 

[TheoMcCloskey]

By inspection we can see x=0 is a solution. Do you have any reasoning to believe there are other solutions?

Edit = maybe I was to hasty - there seems that there is at least one more solution.

 

[HallsofIvy]

3(e^{x}-1)-xe^{x}=0 I do not believe you can solve this one algebraically, one can only approximate the solution to these kind of equations.

can you help me using the latex

If you click on the formula, you will see the code in a new window.

 

[hamamo]

tanx for the reply
the 0 solution i know about it
and there is another solution if you graph the equation you can find it approximately
its about 2.something

 

[hamamo]

by the way
this equation is a result for the Blanck's low and Wien's displacement low
i want to calculate the Wien's constant at the maximum wave length of black body radiation
so
i differentiate Blanck's low and solve the equation for which x have a maximum value
and the result is something like this equation
which now i need to solve for x to find max and min value

 

[coomast]

thanx for the reply up there
but i search more and i found this kind of equation can be solved using
Lambart w-function
or omega function, the problem i couldn't have more information about this function else some expansion series and i can't even write a code to solve or to find a value in lambart function
any more help will be useful
thanx

Hello Hamamo, if you want some code to calculate the Lambert W function, you might consider using the definition of it and the method of Newton-Raphson. The definition as you might know is:

X=Ye^Y \qquad \rightarrow \qquad Y=W(X)

Thus if you define a function f as:

f=Ye^Y-X

You can use the method of Newton Raphson to be for calculating this function:

Y_{n+1}=Y_n-\frac{Y_ne^{Y_n}-X}{e^{Y_n}(Y_n+1)}

Or:

Y_{n+1}=\frac{e^{Y_n}Y_n^2+X}{e^{Y_n}(Y_n+1)}

Take 0 as start value and use this iterative scheme to calculate the solution as the resulting value of the Lambert W function. It converges extremely fast. 5 iterations for the value of the function you are looking to solve.

best regards, Coomast

[Edit] The results of the iteration if you use it on your function:
step n Yn Yn+1
1 0 -0.149361
2 -0.149361 -0.177647
3 -0.177647 -0.178560
4 -0.178560 -0.178561
5 -0.178561 -0.178561

Which is x-3, thus x=2.821439 is the one you need

 

[hamamo]

thanx coomast
you r helpfull that's what i need
thanx again