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 ${\log _e}\left( {{{a + b} \over 2}} \right) = {1 \over 2}({\log _e}a + {\log _e}b)$, then relation between $a$ and $b$ will be
If ${\log _{0.04}}(x - 1) \ge {\log _{0.2}}(x - 1)$ then $x$ belongs to the interval
If $x = {\log _3}5,\,\,\,y = {\log _{17}}25,$ which one of the following is correct
If $\log x:\log y:\log z = (y - z)\,:\,(z - x):(x - y)$ 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