${\log _4}18$ is

The value of $6+\log _{\frac{3}{2}}\left(\frac{1}{3 \sqrt{2}} \sqrt{4-\frac{1}{3 \sqrt{2}} \sqrt{4-\frac{1}{3 \sqrt{2}} \sqrt{4-\frac{1}{3 \sqrt{2}} \ldots}}}\right)$ is

$\sum\limits_{r = 1}^{89} {{{\log }_3}(\tan \,\,{r^o})} = $

For $y = {\log _a}x$ to be defined $'a'$ must be

If ${\log _{10}}2 = 0.30103,{\log _{10}}3 = 0.47712,$ the number of digits in ${3^{12}} \times {2^8} $ is

If ${\log _{10}}x + {\log _{10}}\,y = 2$ then the smallest possible value of $(x + y)$ is