How Can You Solve the Equation e^x = 5-2x?

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Homework Help Overview

The discussion revolves around solving the equation e^x = 5 - 2x, which involves both exponential and linear components. Participants are exploring methods to isolate x and find a solution.

Discussion Character

  • Exploratory, Problem interpretation, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to apply logarithmic properties to isolate x but expresses uncertainty about manipulating the equation further. Some participants suggest that traditional algebraic methods may not suffice due to the nature of the equation, prompting discussions about numerical solutions and the Lambert W function.

Discussion Status

Participants are actively exploring different approaches to the problem, including numerical methods and graphical solutions. There is an acknowledgment that a straightforward algebraic solution may not be possible, and suggestions for alternative methods are being discussed.

Contextual Notes

Some participants note the potential need for approximations and the context of accuracy required for the solution, indicating that the problem may not require a precise answer.

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I am a little stuck how to solve this equation

e^x = 5-2x?

I did ln e^x = ln (5-2x)

x = ln(5-2x) / ln e
but iam not sure how to bring the other x around to the side with the x to solve the equation?
 
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You can't with the "usual" functions. Since you have x both in the exponent and not, you would have to do a numerical solution or use "Lambert's W function", the inverse function to f(x)= xex.
 
how would you go about doing a numerical solution?
 
Why not try it graphically and then do some approximating to find the intercept, e.g. decimal search. This would work if you did not need a highly accurate solution, e.g. in terms of Pi.

The Bob (2004 ©)
 

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