The value of ${(0.05)^{{{\log }_{_{\sqrt {20} }}}(0.1 + 0.01 + 0.001 + ......)}}$ is

Let $S$ be the sum of the digits of the number $15^2 \times 5^{18}$ in base $10$. Then,

If $a = {\log _{24}}12,\,b = {\log _{36}}24$ and $c = {\log _{48}}36,$ then $1+abc$ is equal to

If ${{\log x} \over {b - c}} = {{\log y} \over {c - a}} = {{\log z} \over {a - b}},$ then which of the following is true

If $x = {\log _b}a,\,\,y = {\log _c}b,\,\,\,z = {\log _a}c$, then $xyz$ is

The set of real values of $x$ for which ${2^{{{\log }_{\sqrt 2 }}(x - 1)}} > x + 5$ is