leaks are very deceiving and finding the origin usually is NO where the point of the leak, its usually way up on the pitch.
MOST log homes are constructed with "D" logs and they are kind of "tounge and grooved".
Walls can and do leak if the construction was not done by knowldegable erectors.
Normally on "D" logs with toung and groove, you dry fit the log then remove it and load that groove with tons of liquid nails, then drive a 60D pole barn nail every two feet along that run and off set from the preceding log. This seats the log, secures the log and makes for a secure seal.
This is how Satterwhite Log Home Contractors build this log home. www.satterwhiteloghomes.com or www.satterwhite.com