Given, $k_1 = 10^{16} e^{-2000/T}$ $k_2 = 10^{15} e^{-1000/T}$ When $k_1 = k_2$: $10^{16} e^{-2000/T} = 10^{15} e^{-1000/T}$ $\frac{10^{16}}{10^{15}} = \frac{e^{-1000/T}}{e^{-2000/T}}$ $10 = e^{1000/T}$ Taking natural logarithm ($\ln$) on both sides: $\ln(10) = \frac{1000}{T}$ We know that $\ln(10) = 2.303 \log_{10}(10) = 2.303 \times 1 = 2.303$. Therefore, $2.303 = \frac{1000}{T} \implies T = \frac{1000}{2.303} \text{ K}$.