If ${\log _5}a.{\log _a}x = 2,$then $x$ is equal to
$125$
${a^2}$
$25$
None of these
Let $a, b, x$ be positive real numbers with $a \neq 1$, $x \neq 1$, ab $\neq 1$. Suppose $\log _{ a } b =10$, and $\frac{\log _{ a } x \log _{ x }\left(\frac{ b }{ a }\right)}{\log _{ x } b \log _{ ab } x }=\frac{ p }{ q }$, where $p$ and $q$ are positive integers which are coprime. Then $p+q$ is
The interval of $x$ in which the inequality ${5^{(1/4)(\log _5^2x)}}\, \geqslant \,5{x^{(1/5)(\log _5^x)}}$
${\log _7}{\log _7}\sqrt {7(\sqrt {7\sqrt 7 } )} = $
The solution of the equation ${\log _7}{\log _5}$ $(\sqrt {{x^2} + 5 + x} ) = 0$
If ${\log _{10}}3 = 0.477$, the number of digits in ${3^{40}}$ is