Which is the correct order for a given number $\alpha $in increasing order
${\log _2}\alpha ,\,{\log _3}\alpha ,\,{\log _e}\alpha ,\,{\log _{10}}\alpha $
${\log _{10}}\alpha ,\,{\log _3}\alpha ,{\log _e}\alpha ,{\log _2}\alpha $
${\log _{10}}\alpha ,\,{\log _e}\alpha ,\,{\log _2}\alpha ,\,{\log _3}\alpha $
${\log _3}\alpha ,\,{\log _e}\alpha ,\,{\log _2}\alpha ,\,{\log _{10}}\alpha $
The value of ${81^{(1/{{\log }_5}3)}} + {27^{{{\log }_{_9}}36}} + {3^{4/{{\log }_{_7}}9}}$ is equal to
$\log ab - \log |b| = $
The number of integral solutions $x$ of $\log _{\left(x+\frac{7}{2}\right)}\left(\frac{x-7}{2 x-3}\right)^2 \geq 0$ is
If ${\log _{0.04}}(x - 1) \ge {\log _{0.2}}(x - 1)$ then $x$ belongs to the interval
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