The value of $\sqrt {(\log _{0.5}^24)} $ is
$-2$
$\sqrt {( - 4)} $
$2$
None of these
If ${\log _{10}}3 = 0.477$, the number of digits in ${3^{40}}$ is
If $x, y, z \in R^+$ are such that $z > y > x > 1$ , ${\log _y}x + {\log _x}y = \frac{5}{2}$ and ${\log _z}y + {\log _y}z = \frac{{10}}{3}$ then ${\log _x}z$ is equal to
If ${1 \over {{{\log }_3}\pi }} + {1 \over {{{\log }_4}\pi }} > x,$ then $x$ be
If $a = {\log _{24}}12,\,b = {\log _{36}}24$ and $c = {\log _{48}}36,$ then $1+abc$ is equal to
The number ${\log _2}7$ is