In order to decrease radioactive nuclei to one million of its initial number, number of half - lives required is

$\frac{\mathrm{N}}{{\mathrm{N}}_0}=\frac{1}{2^{\mathrm{n}}}=\frac{1}{{10}^6};2^{\mathrm{n}}={10}^6$
take log on both sides ${\log }_{\mathrm{e}}{2}^{\mathrm{n}}={\log }_{\mathrm{e}}{10}^6$
$\begin{array}{l}{\log }_{10}{2}^{\mathrm{n}}={\log }_{10}{10}^6\\ {\mathrm{nlog}}_{10}2=6{\log }_{10}10;\mathrm{n}\times 0.3010=6\\ \mathrm{n}=\frac{6}{0.3010}\approx \frac{6}{0.3}=20\end{array}$