Try solving this log equation using algebra

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SUMMARY

The equation 6 - 2x = 3 * log(x) cannot be solved analytically without graphing. Instead, numerical methods such as Newton's method provide an effective solution. By defining the function f(x) = 3 * log(x) - 6 + 2x and its derivative f'(x) = (3 / (ln(10) * x)) + 2, users can apply iterative techniques to approximate the solution. Starting with a non-zero initial guess allows for convergence to the correct value.

PREREQUISITES
  • Understanding of logarithmic functions and their properties
  • Familiarity with Newton's method for numerical solutions
  • Basic knowledge of calculus, specifically derivatives
  • Proficiency in using iterative algorithms for problem-solving
NEXT STEPS
  • Study the application of Newton's method in solving nonlinear equations
  • Learn about logarithmic differentiation and its uses
  • Explore numerical methods for root-finding beyond Newton's method
  • Investigate the behavior of logarithmic functions in different bases
USEFUL FOR

Mathematicians, students studying calculus, and anyone interested in numerical methods for solving equations.

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6-2x = 3 * log (x)

Is it possible to solve such an equation without graphing?
 
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newcool said:
6-2x = 3 * log (x)

Is it possible to solve such an equation without graphing?


No.Even graphic methods only give an approximate value...

Daniel.
 
try Newton's method (numerical iteration)

[tex]x_{i+1} = x_{i} - \frac{f(x_{i})}{f'(x_{i})}[/tex]. Write the function as

[tex]f(x) = 3\log(x) - 6 + 2x[/tex] and

[tex]f'(x) = \frac{3}{\ln(10)x} + 2[/tex] (the derivative of the function.

Choose a number not zero to start and just iterate away.
 

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