Your log home sounds lovely, although the carpet sounds out of place. We bet all of that wood really completes a very specific look. Can you get oak planks for the living room?You should not feel concerned about the raw wood matching the kitchen because if you go with raw lumber for the living room you can stain the new flooring to match what is in the kitchen. If you really want to get a fresh new look you can refinish the hardwood floor in the kitchen and then stain both rooms the same color.
To get to a fresh surface in the kitchen you should head to your local home center and rent a U-Sander to help get a smooth and even surface. Then be sure to remove all dust from the hardwood floor. Apply your stain, and allow to dry very thoroughly between coats until desired color is achieved. If you don't allow each coat to dry it will become very thick like paint and never dry.
Once completely dry, apply a urethane top coat with a lambs wool type mop. Give the hardwood floor a light sanding between each coat of urethane for a smooth and durable finish. Make sure you really let everything cure before you move furniture back into those rooms. If you enjoy the look of carpeting, remember; a beautiful area rug can truly help complete the look of the room.