已知log12(7)=a,log12(3)=b,试用a,b表示log21(63)
问题描述：
已知log12(7)=a,log12(3)=b,试用a,b表示log21(63)
答
log12(7)=a,log12(3)=b,
相除,得
lg7/lg3=a/b
log21(63)=lg63/lg21=
(lg21+lg3)/lg21=1+lg3/lg21=1+1/(lg21/lg3)
=1+1/(1+lg7/lg3)
=1+1/(1+a/b)
=1+b/(a+b)
=(a+2b)/(a+b)