Logarithm of $32\root 5 \of 4 $ to the base $2\sqrt 2 $ is
$3.6$
$5$
$5.6$
None of these
If $A = {\log _2}{\log _2}{\log _4}256 + 2{\log _{\sqrt 2 \,}}\,2,$ then $A$ is equal to
If ${\log _{10}}3 = 0.477$, the number of digits in ${3^{40}}$ is
The product of all positive real values of $x$ satisfying the equation $x^{\left(16\left(\log _5 x\right)^3-68 \log _5 x\right)}=5^{-16}$is. . . . .
$\sum\limits_{r = 1}^{89} {{{\log }_3}(\tan \,\,{r^o})} = $
The set of real values of $x$ satisfying ${\log _{1/2}}({x^2} - 6x + 12) \ge - 2$ is