That's not entirely accurate. You are right in that when in FULL recovery mode a Database Backup will not mark portions of the log inactive, however Database backups (a.k.a. Full Backups) actually do interact with the Transaction Log. Please read this article for more info:

More on how much transaction log a full backup includes By Paul Randal[/url]

The real question you should be asking is, why is it that I am thinking of shrinking my transaction log? Your database is in FULL recovery mode which means whoever set it up that way either did not answer the question "do I need point in time recovery?" and did not realize the implications of setting up the database in FULL recovery, or, they answered "yes". You need to find out which one. If they answered "yes" then you need to start managing your transaction logs properly.

If they did not know they were choosing the FULL recovery mode, many inexperienced DBAs do not, and you do not need point in time recovery on this database then you can switch the recovery mode to SIMPLE which would allow you to shrink your log file and relieve you of the need to worry about taking transaction log backups ever again.

Please read this article in its entirety: Managing Transaction Logs By Gail Shaw[/url]

Post questions you have about it, or any responses you have received on this thread so far, and we will try to safely help you out of the mess you are in.