The database as a whole can be read-only (sys.databases) or individual files can be read-only.
Aside, why do you have a job shrinking the log? On a dev system I could understand, but on production that's just harmful.
Gail Shaw
Microsoft Certified Master: SQL Server, MVP, M.Sc (Comp Sci)
SQL In The Wild: Discussions on DB performance with occasional diversions into recoverability