Past exam of the short options paper shared by Prelims and Parts A and B of the physics course of the University of Oxford / 2017 / S16 / 2 / 1 / Solution

At half ionization, electron and neutral densities are each $n_0/2$, so the left side of Saha's equation is $n_0/2$. Its logarithm changes by $d\log n_0=(3/2+R/(k_B{T}^{\prime }))d\log T^{\prime }$. To first order,This holds for small fractional changes and the supplied ground-state partition approximation, not an exact finite-difference identity.