The value of ${\log _2}.{\log _3}....{\log _{100}}{100^{{{99}^{{{98}^{{.^{{.^{{{.2}^1}}}}}}}}}}}$ is
$0$
$1$
$2$
$100!$
If ${a^2} + 4{b^2} = 12ab,$ then $\log (a + 2b)$ is
$\sum\limits_{n = 1}^n {{1 \over {{{\log }_{{2^n}}}(a)}}} = $
The number of solution $(s)$ of the equation $log_7(2^x -1) + log_7(2^x -7) = 1$, 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})} = $