How to find the Microsoft Expression Studio 3 production key out

If you get the Microsoft Expression Studio 3 (not a trival version) from MSDN / TechNet subscription or somewhere else, you may not require to enter the production key when installing, since the key is pre-pidded.

Is there any way to find out the production key?

Yes! After installing, just explore to the %temp% folder and open the "XSetup_ExpressionStudio_<Installed Date & Time>.log", such as XSetup_ExpressionStudio_2009_10_22_12_8_50.log. Then search the key word "InstallProofOfPurchase" to find the production key out.