If a number is represented as 1234 in base $x$ and as $1002003004$ in base $y$, what is the relationship between base $x$ and $y$?
Trying to represent both numbers in base $10$ I can see
$1\cdot x^3+2\cdot x^2+3\cdot x +4 \cdot x^0=1 \cdot y^9+2 \cdot y^6+3 \cdot y^3+4 \cdot y^0$
I notice that it seems that base $y$ is a much smaller base or that base $x$ is a cubed version of base $y$. Yet I'm not really sure about this approach.