Is there an Ubuntu update log?

One way would be to obtain a time-stamped list by opening a terminal with CtrlAltT and issuing the command more /var/log/dpkg.log This will give you more information than you are currently asking for. You can narrow the results considerably using grep for example this command shows packages installed/upgraded on my system as of todays date:

grep "2017-08-21" /var/log/dpkg.log | grep "status installed"

2017-08-21 11:44:41 status installed man-db:amd64 2.6.7.1-1ubuntu1
2017-08-21 11:44:41 status installed doc-base:all 0.10.5
2017-08-21 11:44:41 status installed install-info:amd64 5.2.0.dfsg.1-2
2017-08-21 11:44:41 status installed desktop-file-utils:amd64 0.22-1ubuntu1.1
2017-08-21 11:44:41 status installed mime-support:all 3.54ubuntu1.1
2017-08-21 11:44:41 status installed gnome-menus:amd64 3.10.1-0ubuntu2
2017-08-21 11:44:42 status installed bamfdaemon:amd64 0.5.1+14.04.20140409-0ubuntu1
2017-08-21 11:44:42 status installed hicolor-icon-theme:all 0.13-1
2017-08-21 11:44:42 status installed libgraphite2-3:amd64 1.3.10-0ubuntu0.14.04.1
2017-08-21 11:44:42 status installed logrotate:amd64 3.8.7-1ubuntu1.2
2017-08-21 11:44:42 status installed augeas-lenses:all 1.2.0-0ubuntu1.3
2017-08-21 11:44:42 status installed cvs:amd64 2:1.12.13+real-12ubuntu0.1
2017-08-21 11:44:42 status installed landscape-client-ui-install:amd64 14.12-0ubuntu6.14.04
2017-08-21 11:44:43 status installed libaugeas0:amd64 1.2.0-0ubuntu1.3
2017-08-21 11:44:43 status installed libc-bin:amd64 2.19-0ubuntu6.13

If you want to examine the changelog for a specific package that you have installed you can obtain that information with the command sudo apt-get changelog packagename where packagename is the name of the package.

Example:

sudo apt-get changelog logrotate will provide the change log for the package logrotate