The rate of growth of bacteria in a culture is proportional to the number of bacteris present and the bacteria count is 1000 at initial time $t=0$. The number of bacteria is increased by $20 \%$ in 2 hours. If the population of bacteria is 2000 after $\frac{\mathrm{k}}{\log _{\mathrm{e}}\left(\frac{6}{5}\right)}$ hours, then $\left(\frac{k}{\log _e 2}\right)^2$ is equal to