设数列{an}的公比为q(q≠1),利用保比差数列函数的定义,验证数列{lnf(an)}为等差数列,即可得到结论.
【解析】
设数列{an}的公比为q(q≠1)
①由题意,lnf(an)=ln,∴lnf(an+1)-lnf(an)=ln-ln=ln=-lnq是常数,∴数列{lnf(an)}为等差数列,满足题意;
②由题意,lnf(an)=ln,∴lnf(an+1)-lnf(an)=ln-ln=lnq2=2lnq是常数,∴数列{lnf(an)}为等差数列,满足题意;
③由题意,lnf(an)=ln,∴lnf(an+1)-lnf(an)=ln-ln=an+1-an不是常数,∴数列{lnf(an)}不为等差数列,不满足题意;
④由题意,lnf(an)=ln,∴lnf(an+1)-lnf(an)=ln-ln=lnq是常数,∴数列{lnf(an)}为等差数列,满足题意;
综上,为“保比差数列函数”的所有序号为①②④
故选C.