If ${a^x} = b,{b^y} = c,{c^z} = a,$ then value of $xyz$ is
$0$
$1$
$2$
$3$
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 $\log x:\log y:\log z = (y - z)\,:\,(z - x):(x - y)$ then
The solution of the equation ${\log _7}{\log _5}$ $(\sqrt {{x^2} + 5 + x} ) = 0$
Which is the correct order for a given number $\alpha $in increasing order
The value of $6+\log _{\frac{3}{2}}\left(\frac{1}{3 \sqrt{2}} \sqrt{4-\frac{1}{3 \sqrt{2}} \sqrt{4-\frac{1}{3 \sqrt{2}} \sqrt{4-\frac{1}{3 \sqrt{2}} \ldots}}}\right)$ is