Solving Equations of the Form ln(x) = f(x)

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SUMMARY

The equation of the form ln(x) = -x^2 + a*x + b requires numerical approximation techniques for solutions. While the W-function may offer a theoretical approach, practical implementations favor methods such as Brent's method or the cosecant method for finding roots. These numerical methods provide reliable solutions when dealing with non-logarithmic functions on the right side of the equation.

PREREQUISITES
  • Understanding of logarithmic functions and their properties
  • Familiarity with numerical approximation techniques
  • Knowledge of Brent's method for root-finding
  • Basic concepts of the W-function and its applications
NEXT STEPS
  • Research Brent's method for root-finding in numerical analysis
  • Explore the cosecant method for solving transcendental equations
  • Study the applications of the W-function in solving equations
  • Learn about other numerical methods for approximating solutions to non-linear equations
USEFUL FOR

Mathematicians, software developers, and engineers working on numerical analysis or solving complex equations involving logarithmic and polynomial functions.

nunchakula
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Just came across this for a program I'm writing. I need to be able to solve an equation of the form ln(x) =f(x) where f isn't a logarithm. specifically, it's ln(x)=-x^2+ a*x+b.

Is this solvable for x or do I need a numeric approximation?
 
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Hello.

You must use a numerical approximation to solve this equation.

Bye.
 


It may be possible with the W-function, but I'd suggest numerical methods (Brent's method or the cosecant method).
 

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