The problem probably occurred because in order to delete the transaction log you would have had to stop the SQL Server. This causes the buffer pool (cached data and execution plans) to be erased - nothing can be in memory for a process that isn't running anymore. Now that you've restarted your server, all of your execution plans need to be recompiled.
I would also guess that you're running the server with the default transaction log settings wich specify a default size of 1MB for the transaction log and an automatic growth of 10%. These are very bad settings for performance. The transaction log has to 0 out the file when it grows. You can read more about transaction log management in 8 Steps to Better Transaction Log Management and Database Maintenance Best Practices Part III - Transaction Log Maintenance.
The first question is what did you do to the transaction log? You should never delete a transaction log. This is how your database is able to recover from a crash.
The second question is do you have a log backup solution in place? That is the only reason your transaction logs are growing so large. I suggest looking at Ola Hallengren's excellent backup scripts.
Typically, you want to grow your transaction log to a fixed, sane, size to start with and leave it there. This will depend on your database, but in the past I've monitored log file growth over the course of the week with full database backups happening every morning and log file backups running every 15 minutes. Once I've figured out how large the transaction log can get, I size the transaction log to about 15% larger than that (but as a multiple of 8GB).