Let $ (M,g) $ be a two dimensional Riemmanian manifold, with a smooth distance function $ d(x,y) $ for all $ x, y$ in $ M$. The logarithm of the distance function then satisfies $ \Delta \left( \frac{1}{4 \pi} \log(d(x,y)) \right) = \delta(x-y) $, where $ \Delta $ is the laplace operator induced by the metric.
What is the easiest way to show this?