If $x = \log \left( y + \sqrt{y^2 + 1} \right)$, then $y =$

$7^{2 \log _{7} 5}$ is equal to

The solution set of the inequality ${\log _{10}}({x^2} - 2x - 2) \le 0$ is:

The number of solutions of the equation $\log_{7}(2^{x} - 1) + \log_{7}(2^{x} - 7) = 1$ is:

Let $a, b, x$ be positive real numbers with $a \neq 1, x \neq 1, ab \neq 1$. Suppose $\log_{a} b = 10$,and $\frac{\log_{a} x \cdot \log_{x}(\frac{b}{a})}{\log_{x} b \cdot \log_{ab} x} = \frac{p}{q}$,where $p$ and $q$ are positive integers which are coprime. Then $p+q$ 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