Logs are found at the start of the game (CastleMiner Z) and they're found as the trunk of a tree. They're virtually necessary to craft wood, which is the second most important ingredient in making tools, guns, and crates. 1 log block can craft 4 wood blocks. Not only that, as if you have at least one log, you can use it instead of the more rare coal in order to make iron and copper. To put it in terms, find trees, chop the logs, craft the wood.