Differential Equations: JEE Main 2021 Mathematics question

The rate of growth of bacteria in a culture is proportional to the number of bacteria 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 ${k \over {{{\log }_e}\left( {{6 \over 5}} \right)}}$ hours, then ${\left( {{k \over {{{\log }_e}2}}} \right)^2}$ is equal to :