I ran into the same problem and found out that that was actually permissions issue. If the log path is not accessible to the owner of the child process then the log path doesn't exist.
So, here's what I did:
mongod --fork --logpath ~/log/mongodb.log
You can put it in your /var/log directory by changing the permissions to 740 on /var/log
If you want to learn more about it, you can also read the AWS EC2.