Stuck Trying to Re-arrange Variables

In summary, the conversation discusses the difficulty of solving a particular equation algebraically and the suggestion to use numerical methods instead, such as Newton's method. There is also mention of the possibility of finding a solution for a specific value of "k."
  • #1
cgw_niu
3
0
Homework Statement
I need to re-arrange the below statement in terms of "t"
Relevant Equations
Original Equation:

k = 1/[e^(-A*t) - e^(-B*t)]

Where k is a real number and A and B are real numbers > 1
this is as far as I get:
246511
 
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  • #2
Here is the original form of the equation

246512
 
  • #3
I doubt you will find any algebraic solution to that equation.
 
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  • #4
HallsofIvy said:
I doubt you will find any algebraic solution to that equation.
bummer, I am often given the value of "k" but do not know at what time it happens. The only was so far is to plug and play or plot it and get a close estimate for "t". I am by far means no mathematician, but I would think there has to be a way to solve for "t" for a known value of "k". Maybe not though.
 
  • #5
It's easy to solve for t numerically given the other values. A method like Newton's method should converge to a solution rapidly. That's probably what you really want.
 
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Related to Stuck Trying to Re-arrange Variables

1. What is the purpose of rearranging variables?

Rearranging variables allows us to manipulate equations and solve for specific variables, making it easier to analyze and understand the relationship between different quantities.

2. How do I know when to rearrange variables?

Rearranging variables is often necessary when solving equations or working with complex mathematical formulas. It is especially useful when we need to isolate a specific variable or simplify an equation.

3. What are some common techniques for rearranging variables?

Some common techniques for rearranging variables include using inverse operations, factoring, and substitution. It is important to carefully follow the rules of algebra to ensure accurate results.

4. Can rearranging variables change the meaning of an equation?

Yes, rearranging variables can change the meaning of an equation. When manipulating equations, it is important to maintain the equality between both sides of the equation and not change the overall meaning of the equation.

5. How can I check if I rearranged variables correctly?

You can check if you rearranged variables correctly by substituting your values back into the original equation and verifying that both sides are equal. You can also use a calculator or online equation solver to double-check your work.

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