Making "c" the Subject of a=bc(d)^c

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Discussion Overview

The discussion revolves around the challenge of isolating the variable "c" in the equation a = bc(d)^c. Participants explore the feasibility of this task within the realms of algebra and logarithms, considering the constants involved.

Discussion Character

  • Homework-related, Mathematical reasoning, Debate/contested

Main Points Raised

  • One participant expresses uncertainty about the possibility of making "c" the subject of the equation, indicating that their math teacher was unable to provide a solution.
  • Another participant mentions their unsuccessful attempts to solve the equation using logarithms and suggests that it may not be solvable using elementary algebra.
  • A further contribution asks if there are alternative methods to solve the equation, reiterating that "d" and "b" are constants.
  • Another participant asserts that isolating "c" is impossible and states that the Lambert W function is required for such a solution, noting that this function does not have a representation in terms of standard functions.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the solvability of the equation. While some suggest it may be impossible, others are still exploring potential methods.

Contextual Notes

The discussion highlights limitations in standard algebraic methods and the potential need for advanced functions like the Lambert W function, which may not be familiar to all participants.

Einstein's Cat
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Apologises if this question is not appropriate for this thread but it seemed less suitable to the homework thread as I'm not sure whether it's possible (although I'm hopeful that it is). This question is a product of my self- study of maths and that I've already asked my maths teacher; who was unable to answer.

The question is this: how do I make the term "c" the subject of the equation below?

a = bc (d)^c

Many thanks for your time.
 
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Einstein's Cat said:
Apologises if this question is not appropriate for this thread but it seemed less suitable to the homework thread as I'm not sure whether it's possible (although I'm hopeful that it is). This question is a product of my self- study of maths and that I've already asked my maths teacher; who was unable to answer.

The question is this: how do I make the term "c" the subject of the equation below?

a = bc (d)^c

Many thanks for your time.

I was not able to solve this using logarithms. Probably, this is not solvable using elementary algebra.
 
Math_QED said:
I was not able to solve this using logarithms. Probably, this is not solvable using elementary algebra.
Are there any alternative methods in which it could be solved?

Also, I must say that the terms "d" and "b" are constant.
 
Last edited:
What you ask is impossible. It can be proven to be impossible. You need what is called the Lambert W function for this. This function does not have a repesentation in terms of the standard functions. https://en.wikipedia.org/wiki/Lambert_W_function
 
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