The following error is common when trying to run a 64 bit application on a 32 bit (x86 or i386) version of linux
cannot execute binary file: Exec format error
So it seems you have the 32bit (i386) version of Ubuntu and you are trying to run 64bit teamspeak. Open a terminal and execute the following commands:
First command will download the 32 bit (x86) version to your home folder:
wget http://dl.4players.de/ts/releases/3.0.16/TeamSpeak3-Client-linux_x86-3.0.16.run
Next command will run the run file:
sh TeamSpeak3-Client-linux_x86-3.0.16.run
Finally, after you accept the user agreement, run the following command to start teamspeak:
~/TeamSpeak3-Client-linux_x86/ts3client_runscript.sh
Please post any errors, thanks!