How do I solve for K in ln(1-4k) = -6k?

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Homework Help Overview

The discussion revolves around solving the equation ln(1-4k) = -6k for the variable k, which involves logarithmic and exponential functions.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss taking the exponential of both sides to manipulate the equation, with some expressing uncertainty about properties of the exponential function. There is mention of k=0 as a solution, and others suggest the need for advanced methods like the Lambert W function. Numerical methods and graphical approaches are also proposed for finding solutions.

Discussion Status

The discussion is active with various approaches being explored, including algebraic manipulation, numerical solutions, and graphical visualization. Some participants have provided insights into potential methods, but there is no explicit consensus on a single approach.

Contextual Notes

Participants note that algebraic solutions may not be feasible, indicating a potential constraint in the problem-solving process.

CursedAntagonis
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Homework Statement


Trying to solve for K:

ln(1-4k)=-6k


Homework Equations





The Attempt at a Solution


I know that need to take the e of both side, to get 1-4k=e^-6k, but I cannot remember any properties of e to allow me to remove the k from the exponent. Any tips is appreciated.
 
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CursedAntagonis said:

Homework Statement


Trying to solve for K:

ln(1-4k)=-6k


Homework Equations





The Attempt at a Solution


I know that need to take the e of both side, to get 1-4k=e^-6k, but I cannot remember any properties of e to allow me to remove the k from the exponent. Any tips is appreciated.

Clearly, k=0 is a solution.
to find the another solution you need to use an advanced topic:
http://mathworld.wolfram.com/LambertW-Function.html
 
You have to solve it numerically. You can't solve for k algebraically.

You can visualize the solutions by plotting the functions y=1-4k and y=e^-6k and seeing where they intersect.
 
CursedAntagonis said:
the answer is actually 0.1457 m/s.

m/s?? :smile:
 

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