设loga(c),logb(c)是方程x^2-3x+1=0的两根,求logab (abc)的值不要loga/b(c)的值 是求logab (abc)
问题描述:
设loga(c),logb(c)是方程x^2-3x+1=0的两根,求logab (abc)的值
不要loga/b(c)的值 是求logab (abc)
答
log(ab) abc=log(ab) ab+log(ab) c=1+1/log(c)ab=1+1/[log(c) a+log(c) b]=1+1/[1/log(a)c+1/log(b)c]=1+log(a)c×log(b)c/[log(a)c+log(b)c]由韦达定理log(a)c+log(b)c=3, log(a)c×log(b)c=1所以原式=1+1/3=4/3...