“Exit the base and locate your ship to escape.”
Head for the upper level of the round room where you fought Syrok. You will find an open corridor that leads you away from the room. Start straight down it and to the next door.
As soon as the door starts to open, back up. There is a Taken Phalanx waiting for you on the other side. It will loose a blast of energy to push you back if you are already at the door. This can do significant damage and it will very quickly start shooting at you. Head around the corner to the left after that. Expect a lot of enemies to be coming after you. There are a number more Taken Phalanx coming after you. Go around the next corner and you have the odd Legionary and Phalanx fighting Taken Knights.
There are a few things to scan in this room. You will find a small holographic image of the Dreadnaught sitting on the floor.
On the left wall you will find some controls that can be scanned.
This reveals the commander of this outpost suspended their typical operations to investigate a "Trans-Jovian Threat". Head through the door just to the left of this hologram to move forward. First though, head over to the right of the console. There are a few more things to scan and deal with.
Continuing forward be on guard to encounter a pair of Taken Psions. Quickly eliminate them. The start of the same hallway has another hologram that can be scanned for more information. Continue forward and look to the left. You can see a forced open door on the left. This is one path out. Otherwise, backtrack to the broken door to the left of the nearby hologram by the door and press forward.
As you are running, expect to hear from Zavala. Just start and keep running here. This will lead you to the Aerodrome. Head out onto the walkway and start over to the left. You are going to have a big fight on your hands now.