Question

设loga(c),logb(c)是方程x^2-3x+1=0的两根,求loga/b(c)的值

Answer 1

loga(c),logb(c)是方程x^2-3x+1=0的两根

loga(c)+logb(c)=3

loga(c)*logb(c)=1

logc(a)+logc(b)=1/loga(c)+1/logb(c)=[loga(c)+logb(c)]/loga(c)*logb(c)=3

logc(a)*logc(b)=1/loga(c)*1/logb(c)=1

(logc(a)-logc(b))^2

=(logc(a)+logc(b))^2-4logc(a)*logc(b)

=3^2-4*1

=9-4

=5

logc(a)-logc(b)=±√5

loga/b(c)

=lgc/lg(a/b)

=lgc/(lga-lgb)

=1/(lga/lgc-lgb/lgc)

=1/(logc(a)-logc(b))

=1/±√5

=±√5/5