If ${x^{{3 \over 4}{{({{\log }_3}x)}^2} + {{\log }_3}x - {5 \over 4}}} = \sqrt 3 $ then $x$ has
One positive integral value
One irrational value
Two positive rational values
All of These
For $y = {\log _a}x$ to be defined $'a'$ must be
If ${\log _7}2 = m,$ then ${\log _{49}}28$ is equal to
${\log _4}18$ is
Solution set of equation
$\left| {1 - {{\log }_{\frac{1}{6}}}x} \right| + \left| {{{\log }_2}x} \right| + 2 = \left| {3 - {{\log }_{\frac{1}{6}}}x + {{\log }_{\frac{1}{2}}}x} \right|$ is $\left[ {\frac{a}{b},a} \right],a,b, \in N,$ then the value of $(a + b)$ is
The set of real values of $x$ for which ${\log _{0.2}}{{x + 2} \over x} \le 1$ is