若正数a,b,c成等比数列,则下列三数中成等比数列的是alga,lgb,lgcb10^a,10^b,10^cc5^lga,5^lgb,5^lgcd根号a,三次根号b,四次根号c求详解

Question

若正数a,b,c成等比数列,则下列三数中成等比数列的是
a lga,lgb,lgc
b 10^a,10^b,10^c
c 5^lga,5^lgb,5^lgc
d 根号a,三次根号b,四次根号c
求详解

Answer 1

lga,lgb,lgc成等差数列.
若10^a,10^b,10^c成等比数列,则,(10^b)^2=10^(a+c),即2b=a+c,a,b,c成等差数列
若5^lga,5^lgb,5^lgc成等比数列,5^2lgb=5^(1ga+1gc),即lgb^2=lgac,即b^2=ac,所以5^lga,5^lgb,5^lgc成等比数列.
根号a,三次根号b,四次根号c,b^2/3=ac^1/3不等于a^1/2*c^1/4,故不成等比数列.
选C.