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
If ${a^2} + 4{b^2} = 12ab,$ then $\log (a + 2b)$ is
Which is the correct order for a given number $\alpha $in increasing order
$\sum\limits_{n = 1}^n {{1 \over {{{\log }_{{2^n}}}(a)}}} = $
If ${\log _7}2 = m,$ then ${\log _{49}}28$ is equal to
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