If $x = {\log _b}a,\,\,y = {\log _c}b,\,\,\,z = {\log _a}c$, then $xyz$ is
$0$
$1$
$3$
None of these
If $n = 1983!$, then the value of expression $\frac{1}{{{{\log }_2}n}} + \frac{1}{{{{\log }_3}n}} + \frac{1}{{{{\log }_4}n}} + ....... + \frac{1}{{{{\log }_{1983}}n}}$ is equal to
If ${a^x} = b,{b^y} = c,{c^z} = a,$ then value of $xyz$ is
The set of real values of $x$ satisfying ${\log _{1/2}}({x^2} - 6x + 12) \ge - 2$ is
Let $S$ be the sum of the digits of the number $15^2 \times 5^{18}$ in base $10$. Then,
The number of solution of ${\log _2}(x + 5) = 6 - x$ is