Nothing too obvious in that log that you included.
Your 10 year old laptop, probably the original 320 GB hard drive, the RAM is configured a little strangely, but probably not directly affecting anything. Do you get those shutdowns during boot? Probably a failing hard drive.
Do you get random shutdown at random times, not really anything to do with booting?
Is your MBPro quite warm, or even hot when you get a shutdown? Could be a Good Thing™ to run a utility that will show your temps, such as HWMonitor. smcFanControl allows you to change fan speed, and you can check that the fan is effectively cooling your laptop.
But, going back to the hard drive -- (assuming that there's not another hardware problem going on) a good way to treat your MBPro would be to remove that old hard spinning hard drive, and replace with an SATA solid state drive (SSD). If the hard drive is causing issues, the SSD will take care of those, and leave you with a significantly faster MBPro. There is nothing else to say, except to "try it, you will like it"
(And, while you have the bottom cover open to replace the hard drive, you should check that the fan appears to be clean, and that it can turn freely)