Database Log file Backup I was wondering if the Database Backup .bak Contain the Log file.

i found that the space different between the database and backup is form the locked space for the database.
but i didn't found any related posts that says if the log file is in the backup file.
No it isn't. Or at least not in its entirety. 

Part of the transaction log will be included though reflecting concurrent activity during the backup. This is to allow the database to be restored to a transactionally consistent state.

Much more detail in this article by Paul Randal Understanding SQL Server Backups