If $x = {\log _3}5,\,\,\,y = {\log _{17}}25,$ which one of the following is correct
$x < y$
$x = y$
$x > y$
None of these
The set of real values of $x$ for which ${\log _{0.2}}{{x + 2} \over x} \le 1$ is
If ${\log _4}5 = a$ and ${\log _5}6 = b,$ then ${\log _3}2$ is equal to
Let $a=3 \sqrt{2}$ and $b=\frac{1}{5^{\frac{1}{6}} \sqrt{6}}$. If $x, y \in R$ are such that $3 x+2 y=\log _a(18)^{\frac{5}{4}} \text { and }$ $2 x-y=\log _b(\sqrt{1080}),$ then $4 x+5 y$ is equal to. . . .
If ${\log _{12}}27 = a,$ then ${\log _6}16 = $
The number ${\log _{20}}3$ lies in