# Algebra: Is this possible to solve?

1. Aug 12, 2010

### Curl

I came across this type of equation, and somehow I could not figure out how to solve it analytically. I ended up solving it numerically, but now I'm bothered and I want to know if this is possible.

a = (1-exp(b/x) / (1-exp(c/x))

a,b,c, are constants, x is the unknown

2. Aug 12, 2010

### Dickfore

It cannot be solved analytically for general numbers b and c.

EDIT:

suppose you introduce a new variable:

$$y \equiv \exp\left(\frac{b}{x}\right)$$

Then, for the other exponential, you would have:
$$\exp\left(\frac{c}{x}\right) = \exp\left(\frac{c}{b} \, \frac{b}{x}\right) = \left[\exp\left(\frac{b}{x}\right)\right]^{\frac{c}{b}} = y^{c/b}$$

and the equation becomes:

$$a = \frac{1 - y}{1 - y^{c/b}}$$

$$y = 1 - a ( 1 - y^{c/b})$$

Last edited: Aug 12, 2010