The set of real values of $x$ for which ${2^{{{\log }_{\sqrt 2 }}(x - 1)}} > x + 5$ is
$( - \infty ,\, - 1) \cup (4, + \infty )$
$(4, + \infty )$
$( - 1,\,4)$
None of these
The sum of all the natural numbers for which $log_{(4-x)}(x^2 -14x + 45)$ is defined is -
If ${\log _{1/\sqrt 2 }}\sin x > 0,x \in [0,\,\,4\pi ],$ then the number of values of $x$ which are integral multiples of ${\pi \over 4},$ is
Logarithm of $32\root 5 \of 4 $ to the base $2\sqrt 2 $ is
The solution of the equation ${\log _7}{\log _5}$ $(\sqrt {{x^2} + 5 + x} ) = 0$
The set of real values of $x$ for which ${\log _{0.2}}{{x + 2} \over x} \le 1$ is