Solving Transcendental in Wien's Displacement law

[dcarmichael]

Homework Statement

Solving Transcendental in Wiens Displacement law

Relevant Equations

x=5-e^-x

Hello, I have attached my attempt at a solution. All is okay until i reach x=5-5e^-x. My assignment suggests that i solve it by substituting x=5-ε into the equation where ε is assumed to be small. Solve for ε and then solved for x (Approximate).
Thank you for your help

 

[berkeman]

Homework Statement:: Solving Transcendental in Wiens Displacement law
Relevant Equations:: x=5-e^-x

Hello, I have attached my attempt at a solution. All is okay until i reach x=5-5e^-x. My assignment suggests that i solve it by substituting x=5-ε into the equation where ε is assumed to be small. Solve for ε and then solved for x (Approximate).
Thank you for your help

The attachment appears only to be the problem statement. Did you mean to also attach your work?

Also, your thread title implies that you got a transcendental equation as part of your work. Is that what you mean?

 

[dcarmichael]

The attachment appears only to be the problem statement. Did you mean to also attach your work?

Also, your thread title implies that you got a transcendental equation as part of your work. Is that what you mean?

View attachment 269440

Sorry about that wrong file , I will correct that.

 

[dcarmichael]

Here the file i intended on uploading, ignore the first file as it is irrelevant to the question.

 

[vela]

Substitute in for $x$ to get an expression involving $\varepsilon$. Then expand $e^\varepsilon$ as a series to first order. See where that gets you.

 

[dcarmichael]

Thank you for your help i have figured it out.