If ${a^x} = b,{b^y} = c,{c^z} = a,$ then value of $xyz$ is

If $a = {\log _{24}}12,\,b = {\log _{36}}24$ and $c = {\log _{48}}36,$ then $1+abc$ is equal to

The number of solution pairs $(x, y)$ of the simultaneous equations $\log _{1 / 3}(x+y)+\log _3(x-y)=2$ $2^{y^2}=512^{x+1}$ is

Let $a=3 \sqrt{2}$ and $b=\frac{1}{5^{\frac{1}{6}} \sqrt{6}}$. If $x, y \in R$ are such that  $3 x+2 y=\log _a(18)^{\frac{5}{4}} \text { and }$  $2 x-y=\log _b(\sqrt{1080}),$  then $4 x+5 y$ is equal to. . . . 

The set of real values of $x$ for which ${2^{{{\log }_{\sqrt 2 }}(x - 1)}} > x + 5$ is

If $x = {\log _3}5,\,\,\,y = {\log _{17}}25,$ which one of the following is correct