For two chemical reactions A and B, if the difference between their activation energy is 20 kJ at $300\mathrm{~K}$ $(\mathrm{R} = 8.3\mathrm{~J}\mathrm{~K}^{-1}\mathrm{~mol}^{-1})$.
Determine $\boldsymbol{\operatorname{ln}}\frac{\mathbf{k}_{\mathbf{2}}}{\mathbf{k}_{\mathbf{1}}}$.