Efficient Variable Solving with Maple: Logarithm Properties and Equations

[uman]

Homework Statement

$${\frac {65-75\,{e^{-5\,k}}}{1-{e^{-5\,k}}}}={\frac {60-75\,{e^{-10\,k}<br /> }}{1-{e^{-10\,k}}}}$$

Homework Equations

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

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.

 

[Rainbow Child]

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