(a+b)\ 2 & gt； (ab)^0.5

So LG ((a+b) \ 2) > lg((ab)^0.5)=0.5lg(ab)=0.5(lga+lgb)

Similarly, LG ((C+B) \ 2) > LG ((CB) 0.5) = 0.5 LG (CB) = 0.5 (LGC+LGB).

Similarly, LG ((A+C) \ 2) > LG ((AC) 0.5) = 0.5 LG (AC) = 0.5 (LGA+LGC).

So LG ((a+b) \ 2)+LG ((a+c) \ 2)+LG ((c+b) \ 2) > LGA+LGB+LGC.