Hi Stase,
Your Alt levels are not normal but that doesn't mean you should do Liver Biopsy.
You might want to check the welcome page here:
http://www.medhelp.org/health_pages/Hepatitis/HepB-Introduction--Welcome-Page/show/34?cid=153
Also LOG is one of the units of measurement for hepB DNA: http://www.hepb.org/pdf/hbv_dna.pdf
4 Log seems like 10,000 copies/ml which is not that high. Try to find FIBROSCAN m/c that is an alternative to Liver Biopsy and just like UltraSound (no invasive operation, simple scanning and more effective).
Try to visit a hepatologist (Doctor for Hepatitis) and check for details, you can avoid Liver Biopsy by doing Fibroscan (if needed). Viral load doesn't seem to be high.