The set of real values of $x$ satisfying ${\log _{1/2}}({x^2} - 6x + 12) \ge - 2$ is
$\left( { - \infty ,\,2} \right]$
$[2,\,4]$
$\left[ {4, + \infty } \right)$
None of these
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 ${\log _k}x.\,{\log _5}k = {\log _x}5,k \ne 1,k > 0,$ then $x$ is equal to
If ${\log _{10}}x = y,$ then ${\log _{1000}}{x^2} $ is equal to
Let $S$ be the sum of the digits of the number $15^2 \times 5^{18}$ in base $10$. Then,
The number of real values of the parameter $k$ for which ${({\log _{16}}x)^2} - {\log _{16}}x + {\log _{16}}k = 0$ with real coefficients will have exactly one solution is