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Basic of Logarithms
hard
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
A
$4$
B
$12$
C
$3$
D
None of these
Solution
(a) $0 < {1 \over {\sqrt 2 }} < 1$
${\log _{1/\sqrt 2 }}\sin x > 0$, $x \in [0,\,4\pi ]$$ \Rightarrow $ $0 < \sin x < 1$
$\therefore$ Integral multiple of ${\pi \over 4}$ will be ${\pi \over 4},\,{{3\pi } \over 4},\,{{9\pi } \over 4},{{11\pi } \over 4}$
Number of required values $= 4.$
Standard 11
Mathematics
