Hi Google! It's Robert Hackerman, here with the County Search Engine Inspector Office.
Google: Hi Bob! How can I help you?
Robert: I have a bunch of phrases passed through your Google Translate, can you help me find the IP that submitted them? Thanks.
On a more serious note, if you're going to that level of security, you're probably using something like TOR anyway (otherwise they simply ask the site the text was posted on for the IP). Additionally, you can use multiple services for each translation, obscuring the trail further. Good luck getting that data from Yandex.
Lastly, I'm not sure whether Google (and others) really log every sentence entered, but as described before, you can easily avoid that. Or read the privacy policy.