Find D: [(A - D)^P] / [(B - D)^R] = (C - D)^(P - R)

In summary, the conversation revolves around trying to solve for unknown exponents in equations and creating a general way to do so. The speaker mentions using logs and Pascal's Triangle to solve for these unknowns, and also discusses fitting curves to data points using a simplified equation.
  • #1
Raisintoe
23
2
How do I get D by itself? This one's got me baffled

[(A - D)^P] / [(B - D)^R] = (C - D)^(P - R)
 
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  • #2
Raisintoe said:
How do I get D by itself? This one's got me baffled

[(A - D)^P] / [(B - D)^R] = (C - D)^(P - R)
Take a lotta logs and see if anything shakes out.
 
  • #3
SteamKing said:
Take a lotta logs and see if anything shakes out.
Ha ha ha! I've been to the bathroom enough times while trying to figure this out.
 
  • #4
I have been trying to come up with a definition for Pascal's Triangle so that I can create a general way to solve for unknown exponents. All that I've been able to come up with so far is (1 - N + (N^2 - N)/2 - [1/2∑(n=2 to N) N(N - 2n + 1) + n(n - 1)] . . . ) for Pascal's Triangle of Coeficients
 
  • #5
Raisintoe said:
I have been trying to come up with a definition for Pascal's Triangle so that I can create a general way to solve for unknown exponents. All that I've been able to come up with so far is (1 - N + (N^2 - N)/2 - [1/2∑(n=2 to N) N(N - 2n + 1) + n(n - 1)] . . . ) for Pascal's Triangle of Coeficients
Unknown exponents of what?
 
  • #6
SteamKing said:
Unknown exponents of what?
My exponents, P and R
 
  • #7
Basically you have x^r * y^(p-r) = 1. Without knowing anything about r and p it'll going to be hard. Are you dealing with economic indexes?
 
  • #8
fresh_42 said:
Basically you have x^r * y^(p-r) = 1. Without knowing anything about r and p it'll going to be hard. Are you dealing with economic indexes?
I don't know what economic indexes are, but I am trying to solve for two unknowns in the common equation: V(t) = Vf + (Vi - Vf)*e^(-t/T) where Vf and T are unknown. I am trying to fit this curve to data points that I have collected.
 
  • #9
Raisintoe said:
I don't know what economic indexes are, but I am trying to solve for two unknowns in the common equation: V(t) = Vf + (Vi - Vf)*e^(-t/T) where Vf and T are unknown. I am trying to fit this curve to data points that I have collected.
That's a completely different equation than what you had in the OP.
 
  • #10
SteamKing said:
That's a completely different equation than what you had in the OP.

I want to fit the curve to three points, one point gives my Vi, the other two are my different V(t)s. I simplified to get: T = -t/[ln((V(t) - Vf)/(Hi - Hf))]. Now I can set two equations equal to each other: -ta/[ln((V(ta) - Vf)/(Hi - Hf))] = -tb/[ln((V(tb) - Vf)/(Hi - Hf))].
This simplified to [(H(ta) - Hf)/(Hi - Hf)]^tb = [(H(tb) - Hf)/(Hi - Hf)]^ta. Then [(H(ta) - Hf)^tb]/[(H(tb) - Hf)^ta] = (Hi - Hf)^(tb-ta)
 
  • #11
Raisintoe said:
I have been trying to come up with a definition for Pascal's Triangle so that I can create a general way to solve for unknown exponents. All that I've been able to come up with so far is (1 - N + (N^2 - N)/2 - [1/2∑(n=2 to N) N(N - 2n + 1) + n(n - 1)] . . . ) for Pascal's Triangle of Coeficients
It would help if you could Tex this, making it easier to read.
 

FAQ: Find D: [(A - D)^P] / [(B - D)^R] = (C - D)^(P - R)

What does the equation "Find D: [(A - D)^P] / [(B - D)^R] = (C - D)^(P - R)" represent?

The equation represents a mathematical problem where the goal is to find the value of D that satisfies the equation. The variables A, B, C, P, and R are known values, and D is the unknown value that needs to be determined.

How do you solve the equation "Find D: [(A - D)^P] / [(B - D)^R] = (C - D)^(P - R)"?

To solve the equation, you can use algebraic manipulation and properties of exponents to simplify it and isolate the variable D. This may involve raising both sides of the equation to a power, distributing the exponents, and combining like terms. The resulting equation can then be solved for D using basic arithmetic operations.

Can the equation "Find D: [(A - D)^P] / [(B - D)^R] = (C - D)^(P - R)" have multiple solutions?

Yes, the equation can have multiple solutions, depending on the values of the variables A, B, C, P, and R. In some cases, there may be no real solutions, while in others, there may be an infinite number of solutions. It is important to carefully consider the given values and any restrictions on the variables when solving the equation.

What is the significance of the equation "Find D: [(A - D)^P] / [(B - D)^R] = (C - D)^(P - R)" in scientific research?

The equation may be used in various scientific fields and applications, such as physics, chemistry, and engineering, to calculate unknown values or to model relationships between different quantities. It is also commonly used in data analysis and statistical methods to solve for unknown parameters or to fit data to a specific model.

Are there any real-world examples that can be represented by the equation "Find D: [(A - D)^P] / [(B - D)^R] = (C - D)^(P - R)"?

Yes, the equation can represent various real-world scenarios, such as determining the concentration of a substance in a chemical reaction, calculating the velocity of an object in motion, or finding the optimal solution in a business or economic model. It can also be used to solve problems in areas like population dynamics, genetics, and finance.

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