若三个正数a,b,c成等比数列,三数x,y ,.z 成等差数列,则（y-z)lga+(z-x)lgb+(x-y)lgc=_数学解答

若三个正数a,b,c成等比数列,三数x,y ,.z 成等差数列,则（y-z)lga+(z-x)lgb+(x-y)lgc=

人气：179 ℃　时间：2020-05-24 11:10:46

解答

由题意：b^2 =ac ,2y = x + z 即：y-z = x-y原式=lga^(y-z) + lgb^(z-x) + lgc^(x-y)=lga^(x-y) + lgb^(z-x) + lgc^(x-y) =lg[a^(x-y) × c^(x-y)] + lgb^(z-x)=lg[(ac)^(x-y)] + lgb^(z-x)=lg[(b^2)^(x-y)] +...