In a culture, the bacteria count is $1,00,000.$ The number is increased by $10\%$ in $2$hours.In how many hours will the count reach $2,00,000$ if the rate of growth of bacteria is proportional to the number present?

Question

$\begin{array}{1 1}\large\frac{2.\log 2}{\log(\large\frac{11}{10})} \\ \large\frac{\log 2}{\log(\large\frac{11}{10})} \\\large\frac{2.\log 2}{\log(\large\frac{10}{11})} \\ \large\frac{\log 2}{\log(\large\frac{10}{11})}\end{array}$