When the game is installed it creates two directories. One is the game data, where your exe file is. The other one is the documentation data with save games and the log.html . When you chose the install directory you chose the game data installation folder, while the documentation folder is created automaticaly here C:\ProgramData\Overhype Studios\Battle Brothers . That is where the log file can be found.
C:\ProgramData\Overhype Studios\Battle Brothers\log.html
