Copied and pasted from videogamesblogger guide.

Video Log Location #1 Marine Command Briefing
You can find it in the Mars City reception center. The video can be played on the PDA issued by H.Feiner.

Video Log Location #2 Welcome to Mars Facility One
The footage can be found on the desk placed near H. Feiner present in the Mars City reception.

Video Log Location #3 IPN News Network: Your Universe Now! 11/15/2145
You will find this one in the common area of Mars City. You can’t collect it so, just watch the TV for the length of the entire “IPN News” news report to make it count.

Video Log Location #4 Series 3 Plasma Gun Briefing
In Mars City (combat preparation), the video disk can be found on the reception desk.

Video Log Location #5 Alpha Labs Introduction
In Alpha Labs Hallway (Administration), you can find the log near the data control monitor.

Video Log Location #6 Elemental Phase Deconstructor
In Alpha Labs Sector 1, look for the video log in the EPD lab. You will find it on the desk near the EPD monitor.

Video Log Location #7 Hydrocon
In Alpha Labs Sector 1 (Hydrocon Control), you can find the log on one of the two computer consoles.

Video Log Location #8 Molecular Fuel Storage Compactor
In Alpha Labs Sector 2 (MFS Compressor), the video log is placed on the console.

Video Log Location #9 Mach-2 Chain Gun Briefing
In Alpha Labs Sector 4 (Reactor Sub Station 1), look for the video log on the computer console in the open chamber path.

Video Log Location #10 Maintenance Safety Video
In Monorail Skybridge (Central Maintenance), where else to look except for the computer console.

Video Log Location #11 Medical Report 16-8
In Delta Labs Level 2A (Examination Room D2-1), you will be able to play this video log on a laptop.

Video Log Location #12 Teleportation Experiments
Delta Labs Level 2A (Teleporter Control Lab 2). After returning of the Plasma Inducer, you can find the video log on the desk.

Video Log Location #13 Specimen Stasis Museum
In Data Labs 2B (Lift Access 1), look for the video log on the seats present there.

Video Log Location #14 Soul Cube
In Delta Labs Level 2B (Analysis Control), the disk is on the computer console.

Video Log Location #15 BFG 9000 Briefing
In the Central Server Banks (CPU Access), you will find another computer console with the video disk.

Video Log Location #16 Ancient Civilization
In Site 3 (artifact research), the video log will be found on a computer console.

Video Log Location #17 Tablets
In Caverns Area 2 (Levitation Site), you can find this one on a desk.

Yeah sorry, been busy. ^^;