设loga(m),logb(m)是方程x^2-3x+1=0的两根,试求loga\b(m)的值 答案为+根号5\5或—根号5\5
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![设loga(m),logb(m)是方程x^2-3x+1=0的两根,试求loga\b(m)的值 答案为+根号5\5或—根号5\5](/uploads/image/z/6898218-42-8.jpg?t=%E8%AE%BEloga%28m%29%2Clogb%28m%29%E6%98%AF%E6%96%B9%E7%A8%8Bx%5E2-3x%2B1%3D0%E7%9A%84%E4%B8%A4%E6%A0%B9%2C%E8%AF%95%E6%B1%82loga%5Cb%28m%29%E7%9A%84%E5%80%BC+%E7%AD%94%E6%A1%88%E4%B8%BA%2B%E6%A0%B9%E5%8F%B75%5C5%E6%88%96%E2%80%94%E6%A0%B9%E5%8F%B75%5C5)
设loga(m),logb(m)是方程x^2-3x+1=0的两根,试求loga\b(m)的值 答案为+根号5\5或—根号5\5
设loga(m),logb(m)是方程x^2-3x+1=0的两根,试求loga\b(m)的值
答案为+根号5\5或—根号5\5
设loga(m),logb(m)是方程x^2-3x+1=0的两根,试求loga\b(m)的值 答案为+根号5\5或—根号5\5
loga(m)+logb(m)=3=1/logm(a)+1/logm(b),loga(m)*logb(m)=1=1/[logm(a)*logm(b)],第一个表达式通分得logm(a)+logm(b)=3.于是|logm(a/b)|^2=|logm(a)-logm(b)|^2=(logm(a)+logm(b)^2-4logm(a)*logm(b)=3^2-4=5,因此logm(a/b)=根号(5)或-根号(5),于是loga/b(m)=1/logm(a/b)=1/根号(5)或-1/根号(5).