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 ${1 \over 2} \le {\log _{0.1}}x \le 2$ then
If ${\log _{0.3}}(x - 1) < {\log _{0.09}}(x - 1),$ then $x$ lies in the interval
If $3^x=4^{x-1}$, then $x=$
$(A)$ $\frac{2 \log _3 2}{2 \log _3 2-1}$ $(B)$ $\frac{2}{2-\log _2 3}$ $(C)$ $\frac{1}{1-\log _4 3}$ $(D)$ $\frac{2 \log _2 3}{2 \log _2 3-1}$
${\log _7}{\log _7}\sqrt {7(\sqrt {7\sqrt 7 } )} = $
If $x = {\log _b}a,\,\,y = {\log _c}b,\,\,\,z = {\log _a}c$, then $xyz$ is