设loga(c),logb(c)是方程x^2-3x+1=0的两个根,求loga/b(c)

问题描述:

设loga(c),logb(c)是方程x^2-3x+1=0的两个根,求loga/b(c)

由题意可知
loga(c)+logb(c)=3
loga(c)logb(c)=1,即
1/logc(a)+1/logc(b)=3,即logc(ab)/[logc(a)logc(b)]=3
1/[logc(a)logc(b)]=1
所以logc(ab)=3
logab(c)=1/3