Let $S$ be the sum of the digits of the number $15^2 \times 5^{18}$ in base $10$. Then,
$S < 6$
$6 \leq S < 140$
$140 \leq S < 148$
$S \geq 148$
The set of real values of $x$ satisfying ${\log _{1/2}}({x^2} - 6x + 12) \ge - 2$ is
The number of solution $(s)$ of the equation $log_7(2^x -1) + log_7(2^x -7) = 1$, is -
The number of solution pairs $(x, y)$ of the simultaneous equations $\log _{1 / 3}(x+y)+\log _3(x-y)=2$ $2^{y^2}=512^{x+1}$ is
If $x = {\log _b}a,\,\,y = {\log _c}b,\,\,\,z = {\log _a}c$, then $xyz$ is
The number ${\log _{20}}3$ lies in