If ${\log _{10}}3 = 0.477$, the number of digits in ${3^{40}}$ is
$18$
$19$
$20$
$21$
Let $S$ be the sum of the digits of the number $15^2 \times 5^{18}$ in base $10$. Then,
If ${\log _5}a.{\log _a}x = 2,$then $x$ is equal to
If $a, b, c$ are distinct positive numbers, each different from $1$, such that $[{\log _b}a{\log _c}a - {\log _a}a] + [{\log _a}b{\log _c}b - {\log _b}b]$ $ + [{\log _a}c{\log _b}c - {\log _c}c] = 0,$ then $abc =$
If $A = {\log _2}{\log _2}{\log _4}256 + 2{\log _{\sqrt 2 \,}}\,2,$ then $A$ is equal to
If ${\log _4}5 = a$ and ${\log _5}6 = b,$ then ${\log _3}2$ is equal to