已知lga,lgb,lgc与lga-lg2b,lg2b-lg3c,lg3c-lga依次成等差数列,求a,b,c之比

lga,lgb,lgc成等差数列2lgb=lga+lgclgb^2=lgacb^2=aclga-lg2b,lg2b-lg3c,lg3c-lga依次成等差数列2(lg2b-3c)=(lga-lg2b)+(lg3c-lga)lg2b-lg3c=lg3c-lg2blg2b=lg3c2b=3cb^2=ac=a*2b/3b=2a/3c=2b/3=4a/9a:b:c=1:2/3:4/9...