设logaC,logbC是方程x^2-3x+1=0的两根,求log(a/b) C的值

题目

设logaC,logbC是方程x^2-3x+1=0的两根,求log(a/b) C的值
注(a/b)是下标

答案

logaclogbc=1,logbc-logac=±√(logbc-logac)^2=±√(logbc+logac)^2-4logaclogbc=±√[(3/2)^2-4]=±5/2.
log(a/b) C=1/logc(a/b)=1/(logca-logcb)=1/(1/logac-1/logbc)=logaclogbc/(logbc-logac)=±5/2.