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 ${\log _k}x.\,{\log _5}k = {\log _x}5,k \ne 1,k > 0,$ then $x$ is equal to
Let $S$ be the sum of the digits of the number $15^2 \times 5^{18}$ in base $10$. Then,
${\log _4}18$ is
The value of ${81^{(1/{{\log }_5}3)}} + {27^{{{\log }_{_9}}36}} + {3^{4/{{\log }_{_7}}9}}$ is equal to
The number ${\log _{20}}3$ lies in