$\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
If $a, b, c$ are distinct positive numbers, each different from $1$, such that $[{\log _b}a{\log _c}a - {\log _a}a] + [{\log _a}b{\log _c}b - {\log _b}b]$ $ + [{\log _a}c{\log _b}c - {\log _c}c] = 0,$ then $abc =$
If ${\log _{0.04}}(x - 1) \ge {\log _{0.2}}(x - 1)$ then $x$ belongs to the interval
The sum $\sum \limits_{n=1}^{\infty} \frac{2 n^2+3 n+4}{(2 n) !}$ is equal to :
If $x = {\log _3}5,\,\,\,y = {\log _{17}}25,$ which one of the following is correct
$\log ab - \log |b| = $