$0.5737373...... = $

The number of solutions of $\frac{\log 5 + \log (x^2 + 1)}{\log (x - 2)} = 2$ is

In a right-angled triangle, the sides are $a, b$ and $c$, with $c$ as the hypotenuse, and $c-b \neq 1, c+b \neq 1$. Then the value of $\frac{\log_{c+b} a + \log_{c-b} a}{2 \log_{c+b} a \times \log_{c-b} a}$ is:

If $a_n > 1$ for every $n \in N$,then the minimum value of $\log_{a_2} a_1 + \log_{a_3} a_2 + \dots + \log_{a_n} a_{n-1} + \log_{a_1} a_n$ is:

If $x = \frac{\sqrt{5} + \sqrt{2}}{\sqrt{5} - \sqrt{2}}$ and $y = \frac{\sqrt{5} - \sqrt{2}}{\sqrt{5} + \sqrt{2}}$,then find the value of $3x^2 + 4xy - 3y^2$.

The rational form of the number $1.\overline{41}$ is