The first log you can find is on the first level.
*spoilers*
After waking up on the spaceship, get dressed and talk to the two execs from Wayland. When you talk to the lady who struggles with sleep in space there is a recess with a computer on it. Approach it, and it will prompt you to push A to read the log and achievement unlocked.
For all aliens fans these logs are fantastic references to the original.