If the coefficient n/m is one, is that to be interpreted that Y=X?. If yes, then two laboratories testing the same samples should have a linear relationship btwn the logged Y and logged X with slope one and intercept zero if the accuracy and precision are the same for both laboratories.

Regressing two logged variables against one another does not produce an arithmetic mean regression line. I believe it produces a geometric mean regression line. Does this affect interpretation of n/m?

Graphing logged values against one another tends to conceal differences which is why analytical chemists frown on doing so to demonstrate equality..