How Do I Solve a Logarithmic Equation with Parameters and Find the Value of x?

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Discussion Overview

The discussion revolves around solving the logarithmic equation a*x + b*ln(x) = c, where a, b, and c are parameters. Participants explore various methods for finding the value of x, including numerical techniques and specific mathematical functions.

Discussion Character

  • Exploratory, Technical explanation, Homework-related, Mathematical reasoning

Main Points Raised

  • One participant seeks assistance with the equation and questions whether differential equations are necessary for solving it.
  • Another participant suggests using numerical techniques, specifically mentioning the Newton Raphson method as a suitable approach.
  • A later reply indicates that the Newton Raphson method may require the use of mathematical software to compute results.
  • Another participant counters that a scientific calculator or Excel could suffice for the calculations, implying that extensive iterations may not be necessary.
  • Additionally, a participant introduces the Lambert's W function as a relevant mathematical tool, explaining its definition and potential application in solving the equation.

Areas of Agreement / Disagreement

Participants present multiple approaches to solving the equation, with no consensus on a single method. The discussion remains open to various techniques, including numerical methods and the Lambert's W function.

Contextual Notes

Participants do not clarify the specific conditions under which each method may be applicable, nor do they address potential limitations of the techniques discussed.

abra
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Hi everyone. I'm new in the forum and I'd need an help to solve this equation (sorry, I think it's quite easy but I'm not an expert of mathematics..):

a*x + b*ln(x) = c

where a, b, c are parameters and I need to find the value of x.

Do I need to use techniques of differential equations?

Thanks a lot for any help.
 
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You need to use Numerical Techniques.
Have u come across Newton Raphson method ? It should do just fine on this one.

-- AI
 
No, I've never used the Newton Raphson method.. thanks, i'll have a look to this technique, however, I suppose I need to use some maths softwares to compute the result, isn't it?
 
No. Any scientific calculator will work. You could also use Excel, if you choose.

Hopefully, you won't have to go through too many iterations.
 
There is also the "Lambert's W" function. It is defined specifically as "W(x) is the y satisfying yey= x". In other words, it is the inverse of the function xex.
 

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