Solving e^x = 5-2x: A Step-by-Step Guide

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In summary, the conversation discusses a problem with solving the equation e^x = 5-2x. The individual suggests using ln e^x = ln (5-2x) to solve for x, but is unsure of how to bring the other x to the same side as the x in the exponent. It is mentioned that a numerical solution or Lambert's W function may be necessary, and the individual is advised to try a graphical approach or a decimal search to approximate the intercept if a highly accurate solution is not needed.
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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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  • #2
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.
 
  • #3
how would you go about doing a numerical solution?
 
  • #4
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.

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1. What is the purpose of this guide?

The purpose of this guide is to provide a step-by-step approach to solving the equation e^x = 5-2x. This equation is commonly encountered in mathematical and scientific fields, and this guide aims to help individuals understand and solve it more easily.

2. Who can benefit from this guide?

This guide can benefit anyone who is studying or working in a field that involves mathematical equations, such as physics, chemistry, engineering, or economics. It can also be helpful for students who are learning about exponential functions and their applications.

3. How difficult is it to solve e^x = 5-2x?

The difficulty of solving this equation may vary depending on an individual's mathematical background and familiarity with exponential functions. However, with the step-by-step guide provided, it should be easier for most individuals to understand and solve the equation.

4. Are there any prerequisites for using this guide?

It would be helpful to have a basic understanding of algebra and exponential functions before using this guide. Some knowledge of logarithmic functions may also be beneficial.

5. Can this guide be applied to other similar equations?

Yes, the steps outlined in this guide can be applied to other equations that involve exponential functions and simple algebraic manipulations. However, it may not be applicable to more complex equations or those with multiple variables.

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