Logs block tag isn't working for treecapitator-like axe code

Okay, so I've been trying to make a treecapitator-like axe, but when I do the following procedure it doesn't mine any block except for the one I'm targeting. I've put all logs into the minecraft:logs tag. Is there anything that I'm missing? I also realize this wouldn't exactly be ideal for a treecapitator axe's code, so I would appreciate any insight into how to improve it.