For $y = {\log _a}x$ to be defined $'a'$ must be
Any positive real number
Any number
$ \ge e$
Any positive real number $ \ne 1$
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 -
The interval of $x$ in which the inequality ${5^{(1/4)(\log _5^2x)}}\, \geqslant \,5{x^{(1/5)(\log _5^x)}}$
If ${a^x} = b,{b^y} = c,{c^z} = a,$ then value of $xyz$ is
The number ${\log _{20}}3$ lies in