If the aesthetics concerns you, there are a couple of things you could do.
Soak the log in an antifungal solution for 3 or 4 days. The aim is to kill the mychorrizae or growing threads that have permeated the wood and are slowly breaking it down and feeding on the products there of. Then soak it several changes of hot fresh water for a day or so to remove any residual fungicide.
Alternatively, check out your local aquarium shops for a suitable piece of wood. They have wood which is able to be immersed in water with being prone to breaking down due to fungi or bacteria.
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