log_reuse_Wait_desc always return LOG_BACKUP even right after log backup
When I queried sys.databases to see the log_reuse_Wait_desc it is always LOG_BACKUP- even right after log backup! how do I find why the log_reuse_desc is returning LOG_BACKUP always.

This is nicely explained by Paul Randal:


  Imagine a database where there’s very little insert/update/delete/DDL
  activity, so in between your regular log backups there are only a few
  log records generated, and they’re all in the same VLF. The next log
  backup runs, backing up those few log records, but it can’t clear the
  current VLF, so can’t clear log_reuse_wait_desc. As soon as there are
  enough changes in the database that the current VLF fills up and the
  next VLF is activated, the next log backup should be able to clear the
  previous VLF and then the log_reuse_wait_desc will revert to NOTHING.
  Until the next log backup occurs and isn’t able to clear the current
  VLF, in which case it will go back to LOG_BACKUP again.
  
  So LOG_BACKUP really means “either you need to take a log backup, or
  the log records that were backed up were all in the current VLF and so
  it could not be cleared.”


Full article: Why is log_reuse_wait_desc saying LOG_BACKUP after doing a log backup?

I would like to explore some options to reduce the log file size on the disk.

Before you shrink the log files it is also important for you to understand how you end up with too many or too less number of VLF's. I suggest you read the following posts. These will give you a better idea about VLF and transaction log management.


A Busy/Accidental DBA’s Guide to Managing VLFs by David Levy
How do you clear the SQL Server transaction log? by Aaron Bertrand
Aaron added 4 more links at the bottom of his answer, all those are very useful and related to your question.
Transaction Log VLFs – too many or too few? by Kimberly Tripp