Default, MongoDB creates the log file at this path /var/log/mongodb/mongodb.log, if the log file is not found, please check with the MongoDB config file.

logpath

Check the MongoDB config file at /etc/mongod.conf or /yourMongoDBpath/mongod.conf, the logpath defined where to log.

$ cat /etc/mongod.conf
# mongod.conf
# Where to store the data.
# Note: if you run mongodb as a non-root user (recommended) you may
# need to create and set permissions for this directory manually,
# e.g., if the parent directory isn't mutable by the mongodb user.
dbpath=/var/lib/mongodb3
#where to log
logpath=/var/log/mongodb/mongod.log
#...

References

1. MongoDB – Rotate Log Files
2. MongoDB – mongod options