# Solving Equations

1. Mar 23, 2012

### Tesla.RulZ

1. The problem statement, all variables and given/known data
http://desmond.imageshack.us/Himg191/scaled.php?server=191&filename=daumequation13325015229.png&res=medium [Broken]
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 dont have to itterate them everytime because it's very time consuming and we've got so much work to do.

Last edited by a moderator: May 5, 2017
2. Mar 23, 2012

### 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 = eb , 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.

3. Mar 23, 2012

### 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.