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Rearrange for X - cant seem to make any sense of this problem
Please see attached formula picture. ee(P), ee(S), c and E are variables
I really want to rearrange to ee(P), or ee(S).
I want to make seperate plots of ee(P) and ee(S), where 0 < c < 1, at different values of E from 3 to 200.
However how hard I try to rearrange, I cant seem to get any sense of it.
What I want are two equations of;
ee(P) = a function of C at a specific set E
ee(S) = a function of C at a specific set E
Please help!
Re: Rearrange for X - cant seem to make any sense of this problem
I'm gonna take a stab in the dark here and guess what you're trying to do... (I'm sick and my brain isn't 100% working)
So you want to rearrange this: ![E = \dfrac{\ln[(1-c)(1-ee(S))]}{\ln[(1-c)(1+ee(S))]}](http://latex.codecogs.com/png.latex?E = \dfrac{\ln[(1-c)(1-ee(S))]}{\ln[(1-c)(1+ee(S))]})
and solve for ee(S)??
From the law of logarithms, it can be re-written as: ![E = \ln[(1-c)(1-ee(S)) - (1-c)(1+ee(S))]](http://latex.codecogs.com/png.latex?E = \ln[(1-c)(1-ee(S)) - (1-c)(1+ee(S))])
Then get rid of the logarithm by raising both sides by exp: (1-ee(S)) - (1-c)(1+ee(S)))
Then just expand and solve for ee(S). I think you can carry on from here.
Re: Rearrange for X - cant seem to make any sense of this problem
But what is ee(P)?
-Dan
Edit: Oh, Educated has a typo in there.
@vaffel: When you solve this for, say ee(S), you will have to do it in terms of ee(P). Is this a possible problem?
@Educated: }{ln(b)} \neq ln(a - b))
. The rule you are trying to think of is  - ln(b) = ln \left ( \frac{a}{b} \right ))
- Dan
Re: Rearrange for X - cant seem to make any sense of this problem
I thought it would be easier to state my error here, rather than in my previous post as it is getting cluttered.
I now understand the ee(S) and ee(P) thing. Sorry for the goof!
-Dan
Re: Rearrange for X - cant seem to make any sense of this problem
Me again. :)
These equations can't be solved exactly for ee(S) or ee(P). A quick demonstration with a similar problem will show you why. Solve
}{ln(b)})
 = ln(a))
} = e^{ln(a)})
The LHS can be re-arranged:
} = \left ( e^{ln(b)} \right ) ^E = b^E)
So
In the solution of your problem b = (1 - c)(1 - ee(S)) The ee(S) term is tangled up in the Eth power. There is no exact solution to this equation.
You can still do the graphs, though. Instead of the usual y = f(x) thing you can graph points implicitly. For instance if you want a plot of ee(S) (on the y axis) vs. E (on the x axis) for a particular value of c, pick a value for ee(S), say 3. Then find out what E is for that value. Then plot the point (E, 3). It'll take a lot of graphing single points, but it can be done.
-Dan
Re: Rearrange for X - cant seem to make any sense of this problem
Oh sorry, I clearly did that wrong. I definitely should not be doing math while sick.
Re: Rearrange for X - cant seem to make any sense of this problem
Thanks guys for your answers!
Then my math is not that horrible, as I ended up with the same conclusion as you, topsquarck. I'll see if I can plot the graphs anyways with the method you described.
In the article describing these formulas they say;
"Figure 1 B was computer generated by relating the variables c and ee(P)
in eq 5 to a function of x for values of 0 5 x 5 1; c = 1 - x/2 - xE/2; and
ee(P) = (x - xE)/(2 - x - x E ) . Implicit functions (eq 5 and 6) were solved
by parametric representations."
In here eq 5 and 6 is the same as the equation I posted in the first post.
Maybe Ill figure out how to do this with MATLAB or something!
Re: Rearrange for X - cant seem to make any sense of this problem
Quote:
Originally Posted by
Educated 
Oh sorry, I clearly did that wrong. I definitely should not be doing math while sick.
Pffl. The only reason I can spot the problem that easily is due to the number of times I've done the same thing!
-Dan
Re: Rearrange for X - cant seem to make any sense of this problem
Quote:
Originally Posted by
vaffel Thanks guys for your answers!
Then my math is not that horrible, as I ended up with the same conclusion as you, topsquarck. I'll see if I can plot the graphs anyways with the method you described.
In the article describing these formulas they say;
"Figure 1 B was computer generated by relating the variables c and ee(P)
in eq 5 to a function of x for values of 0 5 x 5 1; c = 1 - x/2 - xE/2; and
ee(P) = (x - xE)/(2 - x - x E ) . Implicit functions (eq 5 and 6) were solved
by parametric representations."
In here eq 5 and 6 is the same as the equation I posted in the first post.
Maybe Ill figure out how to do this with MATLAB or something!
If all you need to do is sketch a graph for given values of c I'd recommend this little graphics plotter. It's not fancy but it gets the job done.
-Dan
