You will note that I didn’t mention that “your log file grew because of a large index rebuild”. That’s because that is probably roughly (this is a really rough rule of thumb) how big your transaction log needs to be. But, anyway, we’re talking about Azure SQL Database, so you don’t need to worry about your transaction log file. Microsoft takes care of that for you: ‘Unlike data files, Azure SQL Database automatically shrinks log files since that operation does not impact database performance.’
Read on for the twist at the end.