What kind of sealer can I use on a log that won't hurt a live plant?

You can use linseed oil. its wood treatment made from natural flax seed,. It has great preservative properties and water resistance. Good luck!!

wax if your making a planter out of log and putting a live plant in it

butcher's wax

transmission fluid

Is it going to be outside in the garden or on a porch or inside? Does the log have an opening in it to accept a plant? or is it just flat? If it is sheltered, no need to seal it. If it is flat, just add a clear plastic tray under the plant. It won't be that noticeable. If it has a hole in it, find a container (maybe recycle a milk carton or something and put the plant in that and then into the log. If you still want to seal it, use Spar varnish.