Given two discrete points on a log-log plot and a defined minimum value on both axes, how would you determine the equation of the line that runs through both points?
I'm aware of how straight lines on a log-log plot are described by monomials, but I'm not sure exactly how to work backwards to that monomial given two points on the line.
Given a power function
$$ y=bx^m $$
graphed on a log-log scale, we have
\begin{eqnarray} \log y&=&m\log x+\log b\\\ Y&=&mX+B \end{eqnarray}
where $Y=\log y$, $X=\log x$, and $B=\log b$.
So given two points $(x_0,y_0)$ and $(x_1,y_1)$ on a log-log graph we have
$$ m=\frac{Y_1-Y_0}{X_1-X_0}=\frac{\log(y_1/y_0)}{\log(x_1/x_0)}\tag{1} $$
And we have
\begin{eqnarray} B&=&Y-mX \tag{2}\\\ \log b&=&\log y-m\log x\\\ b&=&10^{\log y-\log x^m}\\\ b&=&\frac{y}{x^m} \end{eqnarray}
ADDENDUM: Re-reading your question, I think you only need $B$ from equation (2) after finding the value $m$ in equation (1), rather than the value of $b$. You can use $Y=\log y_0$, $X=\log x_0$.