Pictures would really help.
Are the rotten logs all in the same area, or are they diffrent areas around the house?
For the logs that have surface rot, you can patch those with bondo. Get a chisel and remove all the bad wood. You have to get rid of all of it and get down to the solid wood. I use a chisel, the claw of my hammer and anything else I have to remove it. Then I like to use my dremel and a wire wheel on a drill to get it all.
Next, you need to screw in some large wood screws parially into the logs. Make sure the heads of the screws are below the finish level of the logs, but that you have enough threads into the log to give some strength. You can't put in too many, but figure about every four inches, give or take.
Use regular Bondo and mix it in small batches. Just put it onto the log and around the screws. Take your time and let it dry between each layer. Bondo dries fairly quickly, so it wont take long to build up a fair amount of material.
I've done this with gallons of Bondo before, but most of the repairs I've made have been less then a gallon. Don't buy the Walmart version of it, make sure you get the real stuff. There is a big difference.
When you start to get the bondo up to the level of the logs, you can start sanding it with a vibrating sander or an orbital one. I guess you can sand by hand too, but I wouldn't want to. hahaha As you sand, you shape the bondo to match the shape of the log.
Most of the log homes built around here are milled D shape ones. The tops of these are flat, so they fit together good, but they also hold water where they extend past the corners of the home. I've found this to be a place that they rot out first. When I fix these areas, I build up the tops of the logs to give them a round finish to shed water.
After it's all filled in and sanded to shape, I use regular wood stain to finish it off. You have to experimenet with different stains and colors to get the closest match. Don't think of it as stain, but a brown paint. Put it on thick and let it dry on the bondo. The stain will have enough irregular color to it that it will blend in with the logs very nicely. If a client isn't there to see me work on his log home, but comes back after I'm done, they have trouble finding the repair. People who don't know the repair was made will never know by just looking at it. If you look close and know where it was, you'll see it, but that's true with just about any repair.
If you have to remove the entire log, then it gets complicated. The ones I've done have all been in lengths of four feet or less. First I get the old log out by drilling, chiseling and using a sawzall. No chainsaws. I would never use a chainsaw for several reasons. Saftey is one, but control and precision are the biggest concerns. When done, you don't want any other cuts in your remaining logs.
It's improtant to cut the log out as square as possible so the new one fits in nice a tight. This might not work for your logs, but on the ones I've done, I screw on some blocks of wood on the sides of the log right above the one I'm replaceing. I then jack put my jacks under those blocks and lift the wall slightly. You have to judge this, but half to 3/4 of an inch is usually enough.
I then modify the replacement log and existing logs so I can slide the new one into position. When it will fit, I put both liquid nails and silicone all around the log. I like to use plenty of this as it's what's keeping the elements out and the log in place.
After removing the jacks, I can adjust the replacement log with a hammer and block of wood if I have to, but usualy it's pretty close. I finish it off by drilling a few holes into the existing logs and screwing the log into place for insurance. I like to get the screws well below the surface of the existing logs. Sand the logs and fill the holes and gaps with bondo. Sand the bondo and apply stain.
Again, I've had homeowners have to stop and look for the new logs. If you can get the stain to match, it really will make it dificult to tell the new from the old.
Good luck,
Eddie