# Solving for a variable

1. Jan 27, 2008

### uman

1. The problem statement, all variables and given/known data
$${\frac {65-75\,{e^{-5\,k}}}{1-{e^{-5\,k}}}}={\frac {60-75\,{e^{-10\,k} }}{1-{e^{-10\,k}}}}$$

2. Relevant equations
$${e}^{x}=k$$ implies $$x=\ln \left( k \right)$$, as well as other properties of logarithms.

3. The attempt at a solution
Maple makes short work of this, giving $$k=1/5\,\ln \left( 2 \right)$$, but I'm totally lost as to how to solve it myself.

2. Jan 28, 2008

### Rainbow Child

I you set
$$e^{-5\,k}=z$$
then what
$$e^{-10\,k}$$
equals to?