The fundamental solution of the Laplacian, with $(x, y) \in \mathbb{R}^3$, is
$$ \Phi(x, y) = -\frac{1}{4\pi|x - y|} $$ So, say, the further away $x$ is from some point source $y$ the lesser the magnitude of the 'effect' of $\Phi$. And as they become very far apart $\Phi \to 0$.
However for the fundamental solution of the Laplacian, with $(x, y) \in \mathbb{R}^2$, is
$$ \Phi(x, y) = \frac{1}{2\pi}\ln |x - y| $$ This seems to be in conflict with the 3d fundamental solution as now the further apart $x$ and $y$ are the greater the magnitude of the effect of $\Phi$.
Am I missing something here? Intuitively it doesn't seem right that the further we are from some source point, the greater the effect we feel?