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 $x = {\log _b}a,\,\,y = {\log _c}b,\,\,\,z = {\log _a}c$, then $xyz$ is
If ${1 \over 2} \le {\log _{0.1}}x \le 2$ then
If $\log x:\log y:\log z = (y - z)\,:\,(z - x):(x - y)$ then
If $x, y, z \in R^+$ are such that $z > y > x > 1$ , ${\log _y}x + {\log _x}y = \frac{5}{2}$ and ${\log _z}y + {\log _y}z = \frac{{10}}{3}$ then ${\log _x}z$ is equal to
The value of $\sqrt {(\log _{0.5}^24)} $ is