A radioactive nucleus A with a half life T,decays into a nucleus B. At t=0, there is no nucleus B. At sometime t, the ratio of the number of B to that of A is 0.3. Then, t is given by :

Question

$\begin{array}{1 1} (1)t= \large\frac{T}{2} \frac{\log 2}{\log 1.3} \\ (2)\; t= T \frac{\log 1.3}{\log 2} \\ (3)t= T \log (1.3) \\ (4)t= \large\frac{T}{\log (1.3)} \end{array} $