Placing a Birch Log into a furnace while having normal logs in your inventory will not decrement the number of Birch Logs from your inventory. Removing the Birch Log while having another type of Log in your inventory will also remove one normal log and increment the number of Birch Logs.
I have 7 Birch Logs and 5 Normal logs. I place 1 Birch Log into the furnace. My personal inventory reflects no change; I still have 7 Birch Logs and 5 Normal Logs. Removing the Birch Log from the top slot of the Furnace removes 1 Normal Log from my inventory, and increases my Birch Logs by 1. Transversly, placing 1 Normal Log into the top slot of the furnace works as one would expect. 1 Normal Log is taken from my inventory. When removing the Normal Log from the top slot of the Furnace, is it successfully placed back into my Inventory.