Recently I encountered issues starting my TeamSpeak server after updating it from version 3.0.11.4 to 3.0.13.6.; it would immediately crash with a blank error log.
Apparently TeamSpeak Server 3.0.13 onwards requires the 32-bit Visual C++ Redistributable for Visual Studio 2015 to be installed. Yes, the 32-bit variant, even if your OS is 64 bit. So, should you encounter immediate server crashes after updating your TeamSpeak server to version 3.0.13, try downloading and installing the 32-bit variant of Visual Studio 2015 run-time from here: https://www.microsoft.com/en-us/download/details.aspx?id=48145

PS. In case you missed the release notes of TeamSpeak Server 3.0.12, as of that version, the server binaries file names do NOT contain platform suffixes any more. They’re all called “ts3server” now, so don’t forget to delete the old/obsolete binary including the platform suffix from your TeamSpeak Server installation folder (else it will crash as well…)