${\log _4}18$ is
A rational number
An irrational number
A prime number
None of these
If $a = {\log _{24}}12,\,b = {\log _{36}}24$ and $c = {\log _{48}}36,$ then $1+abc$ is equal to
$\sum\limits_{r = 1}^{89} {{{\log }_3}(\tan \,\,{r^o})} = $
If ${\log _{0.04}}(x - 1) \ge {\log _{0.2}}(x - 1)$ then $x$ belongs to the interval
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 $x = {\log _5}(1000)$ and $y = {\log _7}(2058)$ then