1、两边取对数则alga+blgb>algb+blga
不妨设a>b>0,则lga>lgb
由排序不等式alga+blgb>algb+blga
故不等式成立
2、不妨设a>=b>=c,则lga>=lgb>=lgc,所以
alga+blgb+clgc>=blga+clgb+algc
alga+blgb+clgc>=clga+algb+blgc
相加得2alga+2blgb+2clgc>=(b+c)lga+(a+c)lgb+(a+b)lgc
即(a^2a)(b^2b)(c^2c)>=[a^(b+c)][b^(c+a)][c^(a+b)]