Find the domain of the functions z = ln(x2 + y2) and f(x, y) = sqrt(x2 + y2 − 2) / (y - 2).

The natural logarithm $\ln(u)$ is defined only when its argument $u$ is strictly positive.
Therefore, we must have $x^2 + y^2 > 0$.

The expression $x^2 + y^2$ is always non-negative. It is equal to zero only when $x=0$ and $y=0$ simultaneously. For all other points $(x, y)$, $x^2 + y^2$ will be positive.
So, the condition $x^2 + y^2 > 0$ means that $(x, y)$ can be any point in $\mathbb{R}^2$ except for the origin $(0, 0)$.

The domain is $\boxed{\{(x, y) \in \mathbb{R}^2 \mid (x, y) \ne (0, 0)\}}$.

The expression under the square root must be non-negative.

This condition means that the points $(x, y)$ must lie on or outside the circle centered at the origin with radius $\sqrt{2}$.

The denominator cannot be zero.

This condition means that the points $(x, y)$ cannot lie on the line $y=2$.

The domain consists of all points $(x, y)$ such that $x^2 + y^2 \ge 2$ and $y \ne 2$.

The domain is $\boxed{\{(x, y) \in \mathbb{R}^2 \mid x^2 + y^2 \ge 2 \text{ and } y \ne 2\}}$.