I installed mongodb in my mac and following is the way I installed. Where is my mongodb log file located?
$ tar xzf mongodb-osx-x86_64-2.2.3.tgz
$ sudo mv mongod
As @dcrosta answered here: Sane defaults for MongoDB on OSX, MongoDB only have default values for the data path. All other locations shall be established by the user if desired.
In the installation process you posted here, can't see any command to set the log path so, in conclusion, your MongoDB is not saving any log file.