If ${\log _{12}}27 = a,$ then ${\log _6}16 = $
$2.{{3 - a} \over {3 + a}}$
$3.{{3 - a} \over {3 + a}}$
$4.{{3 - a} \over {3 + a}}$
None of these
The value of ${\log _3}\,4{\log _4}\,5{\log _5}\,6{\log _6}\,7{\log _7}\,8{\log _8}\,9$ is
The set of real values of $x$ for which ${\log _{0.2}}{{x + 2} \over x} \le 1$ is
Let $S$ be the sum of the digits of the number $15^2 \times 5^{18}$ in base $10$. Then,
If ${\log _5}a.{\log _a}x = 2,$then $x$ is equal to
The set of real values of $x$ satisfying ${\log _{1/2}}({x^2} - 6x + 12) \ge - 2$ is