$\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
${\log _4}18$ is
The value of ${81^{(1/{{\log }_5}3)}} + {27^{{{\log }_{_9}}36}} + {3^{4/{{\log }_{_7}}9}}$ is equal to
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
If $x = {\log _b}a,\,\,y = {\log _c}b,\,\,\,z = {\log _a}c$, then $xyz$ is
If ${\log _{10}}2 = 0.30103,{\log _{10}}3 = 0.47712,$ the number of digits in ${3^{12}} \times {2^8} $ is