Natural log of a variable times the variable

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Discussion Overview

The discussion revolves around the equation x*ln(2/x) = 5, focusing on methods to solve it. Participants explore algebraic, numerical, and graphical approaches, as well as the existence of solutions, including complex solutions.

Discussion Character

  • Homework-related, Mathematical reasoning, Debate/contested

Main Points Raised

  • One participant seeks guidance on solving the equation x*ln(2/x) = 5, suggesting it may involve a ratio computation.
  • Another participant asserts that the equation cannot be solved algebraically and recommends using software or an iterative technique, mentioning the bisection method as a resource.
  • A repeated inquiry about solving the same equation indicates a persistent interest in finding a solution.
  • One participant claims there are no real solutions to the equation and offers to discuss how to find complex solutions instead.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the existence of solutions, with some asserting no real solutions exist while others are focused on finding a method to solve the equation.

Contextual Notes

The discussion does not clarify the assumptions behind the claims regarding the existence of solutions or the methods proposed for solving the equation.

ill
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so I've got this equation down to

x*ln(2/x) = 5

Can someone show/point me to a page where I can see how to solve this. I am under the impression it requires some type of ratio computation.

thanks!
 
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Last edited:
ill said:
so I've got this equation down to

x*ln(2/x) = 5

Can someone show/point me to a page where I can see how to solve this. I am under the impression it requires some type of ratio computation.

thanks!

(hint: Try graphing the expression on the left.)
 
ill said:
so I've got this equation down to

x*ln(2/x) = 5

There are no real solutions to that equation. Are you interested in how to find the complex solutions?
 

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