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OP keep an eye out for vintage hatchets. They're dirt cheap and are easy to restore into something that ends up better that you'd have to buy premade for $40
worst case scenario all you need is a mustard file to sharpen, small bottle of white vinegar to remove rust, and a log that you can cut down and sand into a handle. Easy peasy.
this thing cost me $15 and two hours work and its literally the best axe