Does backing up a database shrink the transaction log size?
The transaction log file (LDF) is made up of lots of virtual log files (VLFs) inside. Think of it like a cabinet with several pull-out drawers. You could choose a large cabinet, or a small one - but it's still going to be a fixed size with just different numbers of drawers.

As SQL Server works, it puts your transactions into drawers (VLFs.) It starts at one end of your cabinet, fills up the first drawer, then when space runs out in that drawer, it moves on to the next drawer.

When you back up the transaction log, what you're really doing is:


Finding the first drawer that has transactions in it that haven't been backed up yet
Copying those transactions elsewhere
If that drawer is no longer actively in use (because SQL Server has moved on to the next drawer), then you're marking that drawer as available to reuse (think of it as throwing all the contents out)


Backups don't change the size of your cabinet (log file).