If $(\log _{5} x)(\log _{x} 3x)(\log _{3x} y) = \log _{x} x^{3}$, then $y$ equals

If $x_n > x_{n-1} > \dots > x_2 > x_1 > 1$,then the value of $\log_{x_1} \log_{x_2} \log_{x_3} \dots \log_{x_n} (x_n^{x_{n-1}^{\dots^{x_1}}})$ is:

The number of solutions of the equation $\log_{\sqrt{3}}(x^{3} - 1) = \log_{\sqrt{3}}(x - 1) + 2$ is:

If $\log _{2}\left(9^{x-1}+7\right)-\log _{2}\left(3^{x-1}+1\right)=2$,then $x$ values are

If ${a^x} = bc$,${b^y} = ca$,and ${c^z} = ab$,then find the value of $xyz$.

If $x = \log_a(bc)$,$y = \log_b(ca)$,and $z = \log_c(ab)$,then which of the following is equal to $1$?