Solving a Logarithm: Can't Remember How? Try Here!

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Discussion Overview

The discussion revolves around solving the equation x = b/D + a*log(D) for the variable D. Participants explore the complexity of the equation, considering its algebraic and logarithmic components. The scope includes mathematical reasoning and problem-solving strategies.

Discussion Character

  • Mathematical reasoning, Debate/contested

Main Points Raised

  • One participant expresses uncertainty about how to isolate D, questioning whether the problem is too complex for intermediate algebra.
  • Another participant suggests that the equation may not be solvable in terms of elementary functions but proposes the possibility of using the Lambert W function.
  • A later reply introduces the idea of using a Taylor Series expansion as an alternative approach to tackle the problem.

Areas of Agreement / Disagreement

Participants generally agree that the equation is challenging to solve in terms of elementary functions. However, there are competing views regarding the potential methods for finding a solution, such as the Lambert W function and Taylor Series expansion.

Contextual Notes

Participants note that D must be greater than zero, and there is ambiguity regarding the assumptions needed for the proposed methods to be applicable.

natgbz
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Can't remember how to do this (trying to solve for D):

x = b/D + a*log(D)

Any takers? Or is this impossible?
 
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Additive inverse of b/D;
Multiplicative inverse of 'a';

Not sure if the rest is impossible. I'm stuck, since D is the input of the logarithm function and it occurs as a factor too. Am I forgetting something simple, or is this beyond "intermediate" level algebra?
 
symbolipoint said:
Additive inverse of b/D;
Multiplicative inverse of 'a';

Not sure if the rest is impossible. I'm stuck, since D is the input of the logarithm function and it occurs as a factor too. Am I forgetting something simple, or is this beyond "intermediate" level algebra?


Maybe I can simplify the problem here:

a, b, and c are real numbers, D is greater than zero

c = b/D + a*log(D)

how does one solve for D?
 
One doesn't. Not in terms of elementary functions anyway. It might be possible to solve it in terms of the "Lambert W function".
 
HallsofIvy said:
One doesn't. Not in terms of elementary functions anyway. It might be possible to solve it in terms of the "Lambert W function".

How bout a Taylor Series expansion?
 

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