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
The number of solution of ${\log _2}(x + 5) = 6 - x$ is
${\log _4}18$ is
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 $x = {\log _3}5,\,\,\,y = {\log _{17}}25,$ which one of the following is correct
The number ${\log _{20}}3$ lies in