If ${\log _{10}}x = y$,then the value of ${\log _{1000}}{x^2}$ is

If ${x^y} = {y^x}$,then ${(x/y)^{(x/y)}} = {x^{(x/y) - k}}$,where $k = $

If $x = \log_{b}a$,$y = \log_{c}b$,and $z = \log_{a}c$,then the value of $xyz$ is

The number $\log_{20} 3$ lies in

The value of $\left(\left(\log _2 9\right)^2\right)^{\frac{1}{\log _2\left(\log _2 9\right)}} \times(\sqrt{7})^{\frac{1}{\log _4 7}}$ is . . . . . . .

If $n = 1983!$,then the value of the expression $\frac{1}{\log_2 n} + \frac{1}{\log_3 n} + \frac{1}{\log_4 n} + \dots + \frac{1}{\log_{1983} n}$ is: