Question

LOG以a为底C的对数,LOG以b为底C的对数是方程X^2-3X+1=0的两根,求LOG以a/b为底C的对数

Answer 1

设log(a)(C)=m log(b)(C)=n 前一个括号里的是底数,后一个括号了的是真数则m+n=3 mn=1(n-m)²=(m+n)²-4mn=3²-4=5n-m=±√5而log(a/b)(C)=1/log(C)(a/b)=1/[log(C)(a)-log(C)(b)]=1/(1/m-1/n)=mn/(n-m)=...