If ${\log _4}5 = a$ and ${\log _5}6 = b,$ then ${\log _3}2$ is equal to
${1 \over {2a + 1}}$
${1 \over {2b + 1}}$
$2ab + 1$
${1 \over {2ab - 1}}$
The number of solution $(s)$ of the equation $log_7(2^x -1) + log_7(2^x -7) = 1$, is -
If ${1 \over 2} \le {\log _{0.1}}x \le 2$ then
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
The solution of the equation ${\log _7}{\log _5}$ $(\sqrt {{x^2} + 5 + x} ) = 0$
Solution set of inequality ${\log _{10}}({x^2} - 2x - 2) \le 0$ is