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

If ${\log _{12}}27 = a,$ then ${\log _6}16 = $

The roots of the equation $2^{x + 2} \cdot 27^{x/(x - 1)} = 9$ are given by

If $x = \log_a(bc)$,$y = \log_b(ca)$,and $z = \log_c(ab)$,then which of the following is equal to $1$?

The sum of all the natural numbers for which $\log_{(4-x)}(x^2 - 14x + 45)$ is defined is -