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

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In summary, The question asks how to make the term "c" the subject of the equation a = bc (d)^c, but it seems impossible to solve using elementary algebra or logarithms. The Lambert W function is needed for this, but it cannot be represented in terms of standard functions.
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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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  • #2
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.
 
  • #3
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.
 
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  • #4
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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FAQ: Making "c" the Subject of a=bc(d)^c

What is the process for making "c" the subject of the equation a=bc(d)^c?

The process for making "c" the subject of the equation involves isolating "c" on one side of the equation and rearranging the terms to have "c" as the only variable on that side. This can be done by using inverse operations, such as dividing both sides by b and taking the logarithm of both sides.

Why would I want to make "c" the subject of this equation?

Making "c" the subject of the equation allows you to solve for the value of "c" in terms of the other variables. This can be useful in various mathematical and scientific applications, such as finding the optimal value of "c" in a given situation.

What are the steps for solving this equation for "c"?

The steps for solving the equation a=bc(d)^c for "c" involve first isolating "c" on one side of the equation by using inverse operations. This will result in an expression with "c" as the only variable. Then, to solve for "c", you may need to use logarithms or other mathematical techniques depending on the specific form of the equation.

Can I make any variable the subject of this equation, or just "c"?

In general, you can make any variable the subject of an equation as long as it is not a constant. However, the process for making a specific variable the subject may differ depending on the form of the equation and the desired variable. In the equation a=bc(d)^c, "c" is the most natural choice for making the subject due to its position in the equation.

Are there any limitations or restrictions when making "c" the subject of this equation?

The main limitation when making "c" the subject of the equation a=bc(d)^c is that the value of "c" must be nonzero in order for the equation to be solvable. If "c" is equal to 0, the equation becomes a=0, which does not provide any information about the value of "c". Additionally, depending on the values of a, b, and d, there may be multiple or no solutions for "c".

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