SQL Server transaction log growing without control
The only way to "solve" it somehow is backing up 


Because that is the only way to truncate the log. See How to Shrink the SQL Server log for an explanation on what happens. Normally log backups are scheduled very frequently (think 10 minutes) and they truncate the log. You want a frequent log backup not only because it eliminates the growth problem, but primarily because you want to minimize the amount of transactions lost in case of disaster (crash).

If you want a different behavior, change the recovery model to SIMPLE. In case of failure you will loose all the transactions since your last full backup, but there is no free lunch, is there?