If ${\log _{1/\sqrt 2 }}\sin x > 0,x \in [0,\,\,4\pi ],$ then the number of values of $x$ which are integral multiples of ${\pi \over 4},$ is
$4$
$12$
$3$
None of these
The number of solution of ${\log _2}(x + 5) = 6 - x$ is
If ${{\log x} \over {b - c}} = {{\log y} \over {c - a}} = {{\log z} \over {a - b}},$ then which of the following is true
For $y = {\log _a}x$ to be defined $'a'$ must be
If ${\log _4}5 = a$ and ${\log _5}6 = b,$ then ${\log _3}2$ is equal to
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