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
$4$
$12$
$3$
None of these
If ${\log _5}a.{\log _a}x = 2,$then $x$ is equal to
If ${\log _7}2 = m,$ then ${\log _{49}}28$ is equal to
The number of solution $(s)$ of the equation $log_7(2^x -1) + log_7(2^x -7) = 1$, is -
The value of $\left(\left(\log _2 9\right)^2\right)^{\frac{1}{\log _2\left(\log _2 9\right)}} \times(\sqrt{7})^{\frac{1}{\log _4 7}}$ is. . . . . . .
The set of real values of $x$ for which ${\log _{0.2}}{{x + 2} \over x} \le 1$ is