I'm sure what you have written is correct, I'm just having trouble getting from:
[latex]log(y_{1})=rlog(x_{1})+log(c)[/latex]
[latex]log(y_{0})=rlog(x_{0})+log(c)[/latex]
to
[latex]r=\frac{log(\frac{y_{1}}{y_{0}})}{log(\frac{x_{1}} {x_{0}})}[/latex]
Have you done:
[latex]\log(y_0)  r\log(x_0) = \log(y_1)  r\log(x_1)[/latex]
To find r? I don't understand what you mean by interpolating, or what step you did.
