How to increase volume of my turntable - pre-amp - amp setup


Hi. Good Day to you all! My first post and first visit.

I have a cheap Scott turntable equipped with a low priced Audio-Technica mm cartridge through a cheap Berhringer pre-amp into a Logitech Z-680 speaker system. I also have a CD player separately into the system.

The volume output from the speakers is markedly lower from records than from CDs. I suppose that CD medium might be a little louder (the loudness war thing?) than vinyl but this seems to be an output problem not a difference in mediums.

I would like to increase  LP volume. How can I do this? Can I get a higher output cartridge for my turntable? How about a pre-amp with higher output? The Logitech speaker system seems plenty powerful.

I've researched but can't seem to find an answer that I understand. 

Thanks!

128x128rajastrums
I have a cheap Scott turntable equipped with a low priced Audio-Technica mm cartridge through a cheap Berhringer pre-amp into a Logitech Z-680 speaker system. I also have a CD player separately into the system.
If the Berhringer is a phonostage, then I assume all sources are plugged into the Logitech. There are no specs listed, but it accepts line level inputs.
The budget AT carts I looked up are rated at 3.5, 4.2, and 5.0mV at 1 kHz. So it seems that a MM cart into a phonostage with 35dB gain is too low.

https://www.amazon.com/Logitech-Computer-Speakers-5-Speaker-Silver/dp/B00007AKDP
Yes lowrider, I was afraid the OP has one of the budget AT cartridges that had the lower output which would not be suitable for the loudness levels desired with a 35dB gain phonostage. If so, a 5mV cartridge may provide the volume needed but not be equal to the CD player output. A 5mV cartridge and a 40+ dB phonostage would serve much better.  
This is getting a little over-complicated.
The OP has an inexpensive setup. 
Just get this and hook it up and you will be fine. You can always send it back if you don't like it.
https://www.amazon.com/Pro-Ject-Phono-Box-Preamplifier-Black/dp/B01CZW87HS/ref=sr_1_12?s=electronics...
I totally agree that the Pro-Ject is the way to go. When I reread the thread I realized that the Logitech was the only source for power.
What is gain on the ProJect Phono Box? Unless the Box has appreciably more gain than the Behringer how is that going to help?

The answers to each of the OP's questions as posted in 4th paragraph are; yes and yes.  We still don't know what AT cartridge is on the Scott TT, therefore don't know the output.

To me the only complicating issue is the relative cost of adding a vinyl system to an ultra inexpensive computer system. One that can closely match the volume levels provided by a CD player. Not that it can't be done.