I recommend you read Paul Randal's blog about backup myths: http://sqlskills.com/blogs/paul/post/A-SQL-Server-DBA-myth-a-day-(3030)-backup-myths.aspx

30-05) a full or differential backup clears the log

No. A log backup includes all the log since the last log backup - nothing can change that - no matter whether that log was also backed up by a full or differential backup. I had a famous argument on Twitter last year and wrote this blog post as proof: Misconceptions around the log and log backups: how to convince yourself. In the FULL or BULK_LOGGED recovery models, the *only* thing that clears the log is a log backup.