In the standard installation of IIS 7.5 it is not possible to log the incoming requests, not the outgoing responses. The reason for this is probably that Microsoft wants to keep the attack surface as small as possible. But I needed logging so I asked the web master at TMME (thanks Kim) how to do this.

MS’s iis.net offers free extensions: http://www.iis.net/download/AdvancedLogging
http://learn.iis.net/page.aspx/579/advanced-logging-for-iis—custom-logging/

Using the first link to install the Advanced Logging I got an additional icon in the web app properties page:

Possible error:

When opening the “Advanced logging” you’ll see that 1 item is present already. This is defined at site level and inherited to the app level. When you try to modify this item you’ll get:

This is not the most “speaking” error, but it indicates that you’re not supposed to modify at this level. You can either modify the logging at the site level, or create an additional entry for the purposes of your web app.

BTW, the second link explains how to set up the logging, in case you wondered.