Are your abdominals really to blame for your back pain?
In the case of an extension related issue then actually yes, the abdominals are the prime driving force behind control this type of back complaint.
The main point here is to think about what is happening around the low back to create extra load. Again sitting at a desk can cause more issues, tightening hips and mid back forcing more load to be taken through the low back. Generally you will notice pain when;
Standing from sitting
Lying on your front on the floor, or resting on your elbows
Lifting but at the top of the range, standing straight
Carrying a baby
This is not just about making the muscles stronger though. It is about timing, when they engage and how they all work together.
Is this related to your back complaint?