If $x = {\log _b}a,\,\,y = {\log _c}b,\,\,\,z = {\log _a}c$, then $xyz$ is
$0$
$1$
$3$
None of these
Solution set of inequality ${\log _{10}}({x^2} - 2x - 2) \le 0$ is
If ${1 \over 2} \le {\log _{0.1}}x \le 2$ then
The set of real values of $x$ for which ${\log _{0.2}}{{x + 2} \over x} \le 1$ is
If ${x^{{3 \over 4}{{({{\log }_3}x)}^2} + {{\log }_3}x - {5 \over 4}}} = \sqrt 3 $ then $x$ has
Which is the correct order for a given number $\alpha $in increasing order