作业帮上面做的不对。应该用韦达定理的。
来源：学生作业帮 编辑：拍题作业网作业帮 分类：数学作业 时间：2024/04/28 17:37:50
上面做的不对。应该用韦达定理的。
解析,
log(a)c+log(b)c=3,
log(a)c*log(b)c=1,
由于log(a)c,log(b)c≠0,
因此,log(a)c=1/log(c)a,log(b)c=1/log(c)b
故,可以得到,
log(c)a*log(c)b=1,log(c)a+log(c)b=3
log(a/b)c=1/log(c)(a/b)=1/[log(c)a-log(c)b],
又,|log(c)a-log(c)b|=√{[log(c)a+log(c)b]²-4log(c)a*log(c)b}=√5
因此,log(c)a-log(c)b=√5或-√5
故,log(a/b)c=-√5/5或√5/5.
log(a)c+log(b)c=3,
log(a)c*log(b)c=1,
由于log(a)c,log(b)c≠0,
因此,log(a)c=1/log(c)a,log(b)c=1/log(c)b
故,可以得到,
log(c)a*log(c)b=1,log(c)a+log(c)b=3
log(a/b)c=1/log(c)(a/b)=1/[log(c)a-log(c)b],
又,|log(c)a-log(c)b|=√{[log(c)a+log(c)b]²-4log(c)a*log(c)b}=√5
因此,log(c)a-log(c)b=√5或-√5
故,log(a/b)c=-√5/5或√5/5.