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 equation $x^{\frac{3}{4}(\log_2 x)^2 + \log_2 x - \frac{5}{4}} = \sqrt{2}$ has

If $\log _{10} 7 = 0.8451$,then the position of the first significant figure of $7^{-20}$ is

If $\log_e \left( \frac{a + b}{2} \right) = \frac{1}{2}(\log_e a + \log_e b)$,then the relationship between $a$ and $b$ is:

If $a, b, c \neq 0$ and belong to the set $\{0, 1, 2, 3, \ldots, 9\}$, 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 $\log _k x \cdot \log _5 k = \log _x 5$,where $k \neq 1$ and $k > 0$,then the value of $x$ is: