CAT (QA) PYQs

If $x$ is a positive real number such that $4 \log _{10} x+4 \log _{100} x+8 \log _{1000} x=13$, t hen greatest integer not exceeding x , is

The real root of the equation $2^{6x} + 2^{3x+2} - 21 = 0$ is

Let $x$ and $y$ be positive real numbers such that $\log _{5}(x+y)+\log _{5}(x-y)=3$, and $\log _{2} y-\log _{2} x=1-\log _{2} 3$. Then $x y$ equals