Solving Equations: A,B,C,D Constants - Homework Help

[Tesla.RulZ]

Homework Statement

http://desmond.imageshack.us/Himg191/scaled.php?server=191&filename=daumequation13325015229.png&res=medium
where A,B,C & D are constants.

2. The attempt at a solution
Actually i am an electrical engineering student and these 2 equations are transistor equations that we are supposed to itterate in many problems, i tried to solve them but unfortunatley we were never actually taught how to solve Ln equations, so i'd be thankful if someone could solve them so i don't have to itterate them everytime because it's very time consuming and we've got so much work to do.

Thanks in advance !

 

[epenguin]

Do not be afraid to look back in your elementary books.

Inability to solve equations like this = having forgotten what a logarithm is.

If a = e^b , then b = ln a .

This is by definition (or may be - there are various approaches).

When you are revising check out logs to various bases and the relations between them because it looks like you may soon need that.

 

[hunt_mat]

You want to calculate X and Y right, knowing A,B,C and D?

I would get them all in one equation:
$$Y=C\ln\frac{A-Y}{BD}$$
And then write this as:
$$Y-C\ln\frac{A-Y}{BD}=0$$
and use a Newton based scheme to solve it. I would use an initial guess as Y=A/2 because from the equation it is clear that A>Y.
So in this case the Newton scheme would be:
$$Y_{N+1}=Y_{N}-\frac{1+\frac{BCD}{A-Y_{N}}}{Y_{N}-C\ln\frac{A-Y_{N}}{BD}}$$
As a sense check take A=B=C=D=1 and see that the solution is clearly X=1 and Y=0. I took A=2,B=C=D=1 and obtained the solution X=1.5571 and Y=0.44285.