The set of real values of $x$ for which ${2^{{{\log }_{\sqrt 2 }}(x - 1)}} > x + 5$ is
$( - \infty ,\, - 1) \cup (4, + \infty )$
$(4, + \infty )$
$( - 1,\,4)$
None of these
If ${a^x} = b,{b^y} = c,{c^z} = a,$ then value of $xyz$ is
The solution of the equation ${\log _7}{\log _5}$ $(\sqrt {{x^2} + 5 + x} ) = 0$
If $x = {\log _5}(1000)$ and $y = {\log _7}(2058)$ then
If $log_ab + log_bc + log_ca$ vanishes where $a, b$ and $c$ are positive reals different than unity then the value of $(log_ab)^3 + (log_bc)^3 + (log_ca)^3$ is
The number ${\log _2}7$ is