Stoichiometric mixing length L<
sub>
s<
/sub>
of reacting coaxial jet flames is a critical scaling parameter for liquid rocket engine combustors. Previous studies have shown that L<
sub>
s<
/sub>
for shear coaxial flames can be scaled like their non-reacting counterparts using a non-dimensional momentum flux ratio J. In addition, stoichiometric mixing lengths of reacting and nonreacting coaxial jets collapse upon a single line by altering J using an effective outer flow gas density. This effective density is calculated from a modified version of the equivalence principle, originally developed by Tacina and Dahm [1, 2] and accounts for the effects of heat release on mixing. However, previous studies also required a second nonphysical scaling constant S<
sub>
c<
/sub>
for the reacting jets, which is not predicted by the equivalence principle [3]. It was originally hypothesized that S<
sub>
c<
/sub>
is attributed to the limitation of hydroxyl (OH) planar laser-induced fluorescence, which only infers L<
sub>
s<
/sub>
. Direct quantitative measurement of conserved scalar fields using conventional optical diagnostics is difficult due to the lack of a tracer that easily fluoresces, survives high temperature oxygen flames, and is not dominated by quenching effects. To measure a conserved scalar field, this work implements x-ray fluorescence of Kr and Ar tracers to obtain quantitative mixture fraction fields. From these mixture fraction fields, stoichiometric mixing lengths for two CH<
sub>
4<
/sub>
/O<
sub>
2<
/sub>
flames are calculated and scaled against nonreacting coaxial mixing lengths using the equivalence principle. By directly measuring the stoichiometric mixing length, it is established that the additional constant is a byproduct of the OH measurement technique and the equivalence principle fully captures the scaling. Finally, comparison with high-fidelity simulation of the flame further supports this conclusion. In addition to further strengthening this scaling method, this work represents the first use of x-ray fluorescence to make quantitative conserved scalar measurements in turbulent flames.