You simply must get some answers to accurately resolve this:

1) What is the recovery model for your database? Bulk-logged, Full or Simple?

2) If not simple, at what time(s) during the day are log files backed up?

3) What is the specific growth setting on your log file? 10%, 1MB, 20MB, what?

4) What is the specific growth setting on your data file? 10%, 1MB, 20MB, what?

5) Do they ever shrink the log file? (Not truncate, shrink.)

6) Do they rebuild indexes? If so, how often? And do they use SORT_IN_TEMPDB = OFF or ON when they do? [If it's OFF, are they willing to change it to use ON when do your db maintenance? This is highly technical, but it can make a huge difference in how much extra your db will grow during a rebuild.]