Yes. It is an important issue that you need to be deliberate about. Either you store the logs and back them up because you need to, or you put the database in simple recovery mode (no log) and you back up the whole thing.
We had databases that were in full recover mode (because the backup software gave an "error" if they weren't in that mode) but they were never backed up. IT couldn't figure out why their database server kept running out of storage when the database had only 200 MB of data in it. The log was over 20 GB!
If you aren't backing up the log, then it isn't doing you much good. There's the odd chance that the server crashes before a log entry can be commited to disk, but really it's a huge storage price to pay for very little effect.