 Two-temperature Arrhenius extrapolation

For a constant-parameter Arrhenius equation $R(T)=A{e}^{-\beta /T}$ at positive absolute temperatures, subtracting logarithms eliminates the Arrhenius prefactor. The ratio of the two resulting equations gives the displayed prediction. It applies to a reaction rate only when composition and other factors relating rate to the rate constant are held fixed. Equal increments of temperature do not give equal multiplicative rate changes, since the linear variable is $1/T$.