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 number of real values of the parameter $k$ for which ${({\log _{16}}x)^2} - {\log _{16}}x + {\log _{16}}k = 0$ with real coefficients will have exactly one solution is
For $y = {\log _a}x$ to be defined $'a'$ must be
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 $x = {\log _3}5,\,\,\,y = {\log _{17}}25,$ which one of the following is correct
If $x = {\log _5}(1000)$ and $y = {\log _7}(2058)$ then