Answer
$(x,y)=${$10000,5$}
Work Step by Step
Since, we have two equations $2 \log x=y+3$ and $\log x=y-1$
Thus, $2 (y-1)=y+3$
or, $y=5$
Now, $\log x=y-1$
or, $\log x=5-1 \implies 10^4=x$
and $x=10000$
Hence, $(x,y)=${$10000,5$}