The only way to get Dolby 5.1 audio out of the Xbox will be via fiber optic cable from the Xbox to a Dolby Digital amplifier - which will output a decoded 5.1 signal to a 6 channel amplifier and 5 speakers and one sub-woofer. I doubt the Logitech speaker system has a Dolby 5.1 decoder built in with the amplifier for under $100, but I can't say for sure. If the Logitech has a an optical (or TOSLink) input, connect it to the Xbox and follow the instructions below.
To configure your audio settings, follow these steps:
- Start the Xbox 360 console without a disc in the disc tray.
- In the System section of the Xbox Dashboard, select Console Settings.
- In the Console Settings area, select Audio.
- In the Audio Settings area, configure settings for analog output or digital output:
- Analog output settings:
- Dolby Pro Logic II: Select this setting for stereo systems or Dolby Pro Logic II-compatible systems.
- Mono: Select this setting for systems that do not support stereo output.
Note If you have connected to Xbox LIVE and downloaded any AutoUpdates, the Mono option will not be available.
- Digital output settings:
- Digital Stereo: Select this setting to use digital stereo output.
- Dolby Digital 5.1: Select this setting to use Dolby Digital output.
- Enable WMA Pro: Select this setting to enable WMA Pro pass-through if your receiver supports the WMA Pro format.
You must use one of the following cables to support digital output:
- Xbox 360 Component HD AV Cable
- VGA HD AV cable
- S-video AV cable
- Advanced SCART AV cable
- Japanese HDAV D-connector AV cable