$\sum\limits_{n = 1}^n {{1 \over {{{\log }_{{2^n}}}(a)}}} = $
${{n(n + 1)} \over 2}{\log _a}2$
${{n(n + 1)} \over 2}{\log _2}a$
${{{{(n + 1)}^2}{n^2}} \over 4}{\log _2}a$
None of these
Let $\left(x_0, y_0\right)$ be the solution of the following equations $(2 x)^{\ln 2} =(3 y)^{\ln 3}$ $3^{\ln x} =2^{\ln y}$ . Then $x_0$ is
$\sum\limits_{r = 1}^{89} {{{\log }_3}(\tan \,\,{r^o})} = $
If ${\log _{0.3}}(x - 1) < {\log _{0.09}}(x - 1),$ then $x$ lies in the interval
If ${\log _7}2 = m,$ then ${\log _{49}}28$ is equal to
${\log _7}{\log _7}\sqrt {7(\sqrt {7\sqrt 7 } )} = $