Not a single log, but successful logins are logged in /var/log/wtmp and unsuccessful ones in /var/log/btmp. These are binary files, but are readable via the last and lastb commands. From man last:

DESCRIPTION

       last  searches  back through the /var/log/wtmp file (or the file desig‐

       nated by the -f option) and displays a list of all users logged in (and

       out)  since  that  file was created.

and

       lastb is the same as last, except that by default it shows a log of the

       /var/log/btmp file, which contains all the bad login attempts.

Note that access to the btmp (failed login) file is restricted for security reasons: while neither file records password strings by design, a not uncommon cause of failed logins is when users mistakenly type their password into the login field. Hence sudo is needed when running lastb.

Also note that the files are rotated - you may wish to look back through earlier logs ex.

sudo lastb -f /var/log/btmp.1