The value of ${81^{(1/{{\log }_5}3)}} + {27^{{{\log }_{_9}}36}} + {3^{4/{{\log }_{_7}}9}}$ is equal to
$49$
$625$
$216$
$890$
If $\log x:\log y:\log z = (y - z)\,:\,(z - x):(x - y)$ then
${\log _7}{\log _7}\sqrt {7(\sqrt {7\sqrt 7 } )} = $
If $x = {\log _5}(1000)$ and $y = {\log _7}(2058)$ then
If ${\log _5}a.{\log _a}x = 2,$then $x$ is equal to
If ${\log _{\tan {{30}^ \circ }}}\left( {\frac{{2{{\left| z \right|}^2} + 2\left| z \right| - 3}}{{\left| z \right| + 1}}} \right)\, < \, - 2$ then