If $\log _{0.3}(x-1) < \log _{0.09}(x-1),$ then $x$ lies in the interval

$\operatorname{coth}^{-1} 3 + \tanh^{-1} \frac{1}{3} - \operatorname{cosech}^{-1}(-\sqrt{3}) = $

If $A = \log _2 \log _2 \log _4 256 + 2 \log _{\sqrt{2}} 2$,then $A$ is equal to

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 equal to

If $x = \log_{0.1} 0.001$ and $y = \log_9 81$, then $\sqrt{x - 2\sqrt{y}}$ is equal to

The sum of the roots of the equation $x+1-2 \log _{2}\left(3+2^{x}\right)+2 \log _{4}\left(10-2^{-x}\right)=0$ is: