How to Solve for Unknown Variable in ln Equation?

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SUMMARY

The discussion focuses on solving the equation ln(1-x) - 5x + 7.5 = 0 for the unknown variable x. It is established that due to the presence of x both inside the natural logarithm and outside, traditional algebraic methods are ineffective. Participants agree that numerical methods are necessary to find an approximate solution for x. Tools such as numerical solvers or graphing calculators are recommended for this purpose.

PREREQUISITES
  • Understanding of natural logarithms and their properties
  • Familiarity with transcendental equations
  • Basic knowledge of numerical methods for solving equations
  • Experience with graphing calculators or numerical solver tools
NEXT STEPS
  • Research numerical methods such as the Newton-Raphson method
  • Learn how to use graphing calculators to solve transcendental equations
  • Explore software tools like MATLAB or Python's SciPy library for numerical solutions
  • Study the properties and applications of natural logarithms in equations
USEFUL FOR

Students studying calculus, mathematicians dealing with transcendental equations, and anyone interested in numerical methods for solving complex equations.

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Homework Statement



I've been puzzling with this for 1 hour and can't figure it out. How do you calculate the unknown x from this equation?

Homework Equations



ln(1-x)-5x+7.5=0
 
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Since this involves the variable, x, both inside a transcendental function and outside it, there is no "algebraic" method to solve for x. You will have to use a numerical method.
 

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