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?