Question

If the mantissa of the ${\log }_{1/3}\sqrt[3]{33}$ is can be expressed as $0.\overline{a}$, then the value of $a$ is

Answer 1

${\log }_{1/3}\sqrt[3]{33}=-{\log }_3\sqrt[3]{33}=-\frac{1}{3}{\log }_{3}3=-\frac{1}{3}=-1+\frac{2}{3}$
Therefore, then mantissa is $\frac{2}{3}=0.\overline{6}$
Hence, $a=6$