Solution of an exponential equation

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SUMMARY

The equation 128b - 127b = 147.058 does not have an analytical solution. Participants in the discussion confirmed that numerical methods, specifically the Bisection method and Newton-Raphson, are the only viable approaches to approximate the solution. The consensus is that attempting to derive an analytical solution is futile, as the nature of the equation does not permit it.

PREREQUISITES
  • Understanding of exponential equations
  • Familiarity with numerical methods, specifically Bisection method and Newton-Raphson
  • Basic knowledge of calculus and function analysis
  • Proficiency in mathematical problem-solving techniques
NEXT STEPS
  • Study the Bisection method for root-finding in numerical analysis
  • Explore the Newton-Raphson method for solving equations
  • Research the limitations of analytical solutions in exponential equations
  • Learn about alternative numerical methods for solving complex equations
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Mathematics students, educators, and anyone interested in numerical methods for solving exponential equations will benefit from this discussion.

Ali Baig
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Homework Statement


I am trying to solve an equation.
128^b - 127^b = 147.058.

Homework Equations

The Attempt at a Solution


I have tried numerical methods like Bisection method and Newton-Raphson, but I need analytical solution.
Thank you.
 
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Ali Baig said:
need analytical solution.
What makes you think there is one?
 
Ali Baig said:

Homework Statement


I am trying to solve an equation.
128^b - 127^b = 147.058.

Homework Equations

The Attempt at a Solution


I have tried numerical methods like Bisection method and Newton-Raphson, but I need analytical solution.
Thank you.

Those are the only methods that will work in this problem. An analytical solution is not possible.
 

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