The set of real values of $x$ for which ${\log _{0.2}}{{x + 2} \over x} \le 1$ is
$\left( { - \infty ,\,\, - {5 \over 2}} \right] \cup (0, + \infty )$
$\left[ {{5 \over 2}, + \,\infty } \right)$
$( - \infty ,\, - 2) \cup (0, + \,\infty )$
None of these
If ${1 \over 2} \le {\log _{0.1}}x \le 2$ then
The number ${\log _2}7$ is
The number of solution pairs $(x, y)$ of the simultaneous equations $\log _{1 / 3}(x+y)+\log _3(x-y)=2$ $2^{y^2}=512^{x+1}$ is
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 $abc =$
${\log _4}18$ is