If $\frac{1}{\log_3 \pi} + \frac{1}{\log_4 \pi} > x$,then $x =$ ?

$x = \log \left( \frac{1}{y} + \sqrt{1 + \frac{1}{y^2}} \right) \Rightarrow y$ is equal to

Given that $a, b \in \{0, 1, 2, \ldots, 9\}$ with $a+b \neq 0$ and that $\left(a+\frac{b}{10}\right)^x = \left(\frac{a}{10}+\frac{b}{100}\right)^y = 1000$. Then,$\frac{1}{x} - \frac{1}{y}$ is equal to

If $x$ satisfies the inequality $\log _{25} x^2 + (\log _5 x)^2 < 2$,then $x$ belongs to

The number of solutions to the equation $\log _2(x + 5) = 6 - x$ is

If $a, b, c \neq 0$ and belong to the set $\{1, 2, 3, \ldots, 9\}$,then $\log _{10}\left(\frac{a+10 b+10^2 c}{10^{-4} a+10^{-3} b+10^{-2} c}\right)$ is equal to