Log date on cell text change. google spreadsheet

I'm trying to log the date in a cell when a user tries to enter a text in another cell. To give you a clearer picture, I would like today's date to be logged in cell B1 when a user writes something in A1. I used this formula in B1:

=IF(A1="","",B1=TODAY())

but it doesn't work! Any idea how I can do this?