Ok, since no one has submitted a guide for this yet, I'll give you guys a quick brief on where all the logs are... Hopefully someone can make a video for this and provide you guys with a proper solution. Until then, enjoy.
gamerboyTHXtss was kind enough to make a video guide for us. Thanks a lot! Makes it so much easier.
Mission 1 -
1) Shortly after hiding in a locker and meeting Stone and Turk you will progress a little further and enter a room with an operating pit on your left and a turret around the corner also on the left. Head straight and in that room is the first audio log. Its next to the vent you have to crawl inside to flank the turret.
2) After you split up from your companions you'll progress a good ways and find yourself in a lot of hallways surrounded by different labs. The second audio log will be in the lab on the left before you go up the stairs to the big hangar where your character says "Level 3 Bay 4". Theres a loading crane arm thing aliens crawl down and attack you when you enter. If you got here without grabbing the second log, you've gone too far.
Mission 2 -
3) The third audio log is right after you and Hicks open the armory and gear up. After accessing the table terminal, you'll go right up the steps. The audio log is right in front of you on the desk in this room.
4) After fighting through a few rooms with aliens in them, you'll pass through a library and then you'll enter a locker room. As you enter the locker room turn left and the log is sitting on a bench.
Mission 3 -
5) Shortly after passing through the hole in the fence, you'll be in an open area with enemies on a catwalk/steps to the right. Head up the stairs on the right and go inside the building the enemies were coming out of and it will be on a computer dash. The exit of this area is a metal container which the enemy will open and attack you. If you pass this point without grabbing the log, turn around. The building will be
on the left if you're back tracking.
6) This one is outside. You will fight on the planets surface for a long ass time and eventually you'll find a lot of containers and the path will bend right. Stick to the right (the high ground) and this audio log will be on top of a box. If you get to the armored vehicle that attacks you, you've gone slightly too far. Turn around and back track, stick to the left.
Mission 4 -
7) Near the very beginning. Head forward towards the tunnel and it will be on the left near a dead body against the wall.
8) After clearing the first egg room and going down the steps and through the orange/red tunnels you'll see this one straight in front of you on a box, along with your next xeno fight.
9) When you get to the door that has a machine stuck in it, you'll enter a gas filled area. Upon entering go up the stairs to your left, and the log is in the room up top on a counter.
10) The final log of this mission and the DLC, is near the last vent you have to open for Hicks. As soon as you come up the steps, hang a left around the corner.