The size of our database file (mdf) is about 14GB. I observed that the log file has grown to 75GB in the recent time. I was presuming that the "full backup" operation would truncate the log file every time it is performed.
No, this is a completely incorrect assumption. You also need to backup the transaction log. And the full/diff backups and the log backups are completely separate.
Today I triggered the backup manually 3 times. The log file remained the same size.
And here is another important piece of information: the log file never shrinks by itself, even if you back up the transaction log. (Unless the database is in autoshrink, but that option is evil from the inside out.)
I think you first should consider what recovery you need. That is, in case of a disaster where your database goes belly-up, do you need be able to restore the database to a certain point in time? Or are you content with restoring the most recent full backup?
Since you don't take log backups, I kind of suspect that the latter applies to you. In this case, set the database to simple recovery, and there is no need for log backups.
If you need point-in-time recovery, you should implement log backups, and your first log backup will be big. :-)
Once you have settled on either of these solutions, you should shrink the log file. Please be aware of that shrinking a file is an exceptional thing to do, and nothing you do by routine (because it also takes resources to grow it again.) But in a case you
have failed to take log backups for a while, you have a good case. Shrink the log file to some reasonable size, 5 GB:
DBCC SHRINKFILE(logfile, 5000)