1.设“以a为底c的对数”与“以b为底c的对数”是方程x^2 -3x+1=0的两根,则求“以a/b为底c的对数”.2.设m是方程lnx+2x-6=0的近似解,且m∈(a,b),b-a=1,求a,b的值.
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![1.设“以a为底c的对数”与“以b为底c的对数”是方程x^2 -3x+1=0的两根,则求“以a/b为底c的对数”.2.设m是方程lnx+2x-6=0的近似解,且m∈(a,b),b-a=1,求a,b的值.](/uploads/image/z/3695556-12-6.jpg?t=1.%E8%AE%BE%E2%80%9C%E4%BB%A5a%E4%B8%BA%E5%BA%95c%E7%9A%84%E5%AF%B9%E6%95%B0%E2%80%9D%E4%B8%8E%E2%80%9C%E4%BB%A5b%E4%B8%BA%E5%BA%95c%E7%9A%84%E5%AF%B9%E6%95%B0%E2%80%9D%E6%98%AF%E6%96%B9%E7%A8%8Bx%5E2+-3x%2B1%3D0%E7%9A%84%E4%B8%A4%E6%A0%B9%2C%E5%88%99%E6%B1%82%E2%80%9C%E4%BB%A5a%2Fb%E4%B8%BA%E5%BA%95c%E7%9A%84%E5%AF%B9%E6%95%B0%E2%80%9D.2.%E8%AE%BEm%E6%98%AF%E6%96%B9%E7%A8%8Blnx%2B2x-6%3D0%E7%9A%84%E8%BF%91%E4%BC%BC%E8%A7%A3%2C%E4%B8%94m%E2%88%88%28a%2Cb%29%2Cb-a%3D1%2C%E6%B1%82a%2Cb%E7%9A%84%E5%80%BC.)
1.设“以a为底c的对数”与“以b为底c的对数”是方程x^2 -3x+1=0的两根,则求“以a/b为底c的对数”.2.设m是方程lnx+2x-6=0的近似解,且m∈(a,b),b-a=1,求a,b的值.
1.设“以a为底c的对数”与“以b为底c的对数”是方程x^2 -3x+1=0的两根,则求“以a/b为底c的对数”.
2.设m是方程lnx+2x-6=0的近似解,且m∈(a,b),b-a=1,求a,b的值.
1.设“以a为底c的对数”与“以b为底c的对数”是方程x^2 -3x+1=0的两根,则求“以a/b为底c的对数”.2.设m是方程lnx+2x-6=0的近似解,且m∈(a,b),b-a=1,求a,b的值.
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=5
n-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)
=1/(n-m)
若n-m=√5,则log(a/b)(C)=1/√5=√5/5
若n-m=-√5,则log(a/b)(C)=1/(-√5)=-√5/5
㏒a C,㏒b C,是方程x^2 -3x+1=0两根,所以㏒a C+㏒b C=3,㏒a C*㏒b C=1
㏒a/b C=(lgC)/(lga/b)=(lgC)/(lga-lgb)
由㏒a C+㏒b C=3得(lgc*lgb+lga*lgc)/lga*lgb=3,由㏒a C*㏒b C=1得lgc*lgc/lga*lgb=1
所以(lgb+lga)/lgc=3,lgb+lga=...
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㏒a C,㏒b C,是方程x^2 -3x+1=0两根,所以㏒a C+㏒b C=3,㏒a C*㏒b C=1
㏒a/b C=(lgC)/(lga/b)=(lgC)/(lga-lgb)
由㏒a C+㏒b C=3得(lgc*lgb+lga*lgc)/lga*lgb=3,由㏒a C*㏒b C=1得lgc*lgc/lga*lgb=1
所以(lgb+lga)/lgc=3,lgb+lga=√(lgb-lga)²-4lgb*lga=√5lgc*lgc
所以㏒a/b C=lgC/√5lgC=√5/5
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