If $\log_{10} 2 = 0.30103$ and $\log_{10} 3 = 0.47712$,then the number of digits in $3^{12} \times 2^8$ is:

The value of $\log_{\frac{1}{8}\csc^2\frac{\pi}{8}} \sin^2\frac{3\pi}{8}$ is equal to

$\tanh^{-1}(\frac{1}{2}) + \operatorname{coth}^{-1}(3) = $

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

The value of $\{x \in R \mid \log_{10} ((1.6)^{1-x^2} - (0.625)^{6(1+x)}) \in R\}$ 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