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

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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
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

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+lgc
lgb^2=lgac
b^2=ac
lga-lg2b,lg2b-lg3c,lg3c-lga依次成等差数列
2(lg2b-3c)=(lga-lg2b)+(lg3c-lga)
lg2b-lg3c=lg3c-lg2b
lg2b=lg3c
2b=3c
b^2=ac=a*2b/3
b=2a/3
c=2b/3=4a/9
a:b:c=1:2/3:4/9=9:6:4