$0.5737373...... = $

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:

The square root of $\frac{(0.75)^3}{1-0.75}+[0.75+(0.75)^2+1]$ is

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

Let $p = 99$ and $q = 101$. Define $p_1 = \log_{10} \left(\frac{p+q}{2}\right)$ and $q_1 = \frac{1}{2}(\log_{10} p + \log_{10} q)$,and $p_2 = \log_{10} \left(\frac{p_1+q_1}{2}\right)$,$q_2 = \frac{1}{2}(\log_{10} p_1 + \log_{10} q_1)$. Then:

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