I have a simple problem of deducing whether the kernel $$k(x,t) := \log |x-t|$$ is weakly singular or not. I have seen many basic examples of how to do this but I can't make the link to this.
I know that the kernel is weakly singular if $$|k(x,t)| \leq C|x-t|^{- \alpha}$$
Does it have something to do with $\log 0$ being undefined and $|x-t| \rightarrow 0$ ? Any help would be appreicated.