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 $
Let $S$ be the sum of the digits of the number $15^2 \times 5^{18}$ in base $10$. 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
Logarithm of $32\root 5 \of 4 $ to the base $2\sqrt 2 $ is
The number of solution $(s)$ of the equation $log_7(2^x -1) + log_7(2^x -7) = 1$, is -
If ${\log _{10}}x + {\log _{10}}\,y = 2$ then the smallest possible value of $(x + y)$ is