Before you complete the mission called Clear the Path in Riven Gate, there are 5 collectibles you can get. This guide will give you the location of all the collectibles you can find in the Riven Gate area.
In the middle of the map in Riven Gate, enter the building with a vehicle parked inside. The 1st Banished Log is on the wall in the room. Go south as shown above and you will find a building near the bridge. The 2nd Banished Log is inside the building on top of the weapon crate.
From the last area, go to your left and follow the hallway until you find a yellow barrier. Expose the Generator in the middle of the room to remove the barrier and you can find the Spartan Core inside.
Go northwest of the Spartan Core and climb up the mountain. On the way up, you will see the UNSC Log on top of a crate. Now follow the road to the east as shown above and you will find the last UNSC log on top of a mountain.