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

If $A = {\log _2}{\log _2}{\log _4}256 + 2{\log _{\sqrt 2 \,}}\,2,$ then $A$ is equal to

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

If ${a^x} = b,{b^y} = c,{c^z} = a,$ then value of $xyz$ is

$\log ab - \log |b| = $

Let $x, y$ be real numbers such that $x>2 y>0$ and $2 \log (x-2 y)=\log x+\log y$  Then, the possible value(s) of $\frac{x}{y}$