已知log以5为底6的对数=a,log以5为底4的 - 知识问答

已知log以5为底6的对数=a,log以5为底4的对数=b.用a.b表示log以25为底12的对数

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log(5)(6)=a
log(5)(2)+log(5)(3)=a
log(5)(4)=b
2log(5)(2)=b
log(5)(2)=b/2
b/2+log(5)(3)=a
解得log(5)(3)=a-b/2
log(25)(12)
=log(25)(3)+log(25)(4)
=log(5²)(3)+log(5²)(2²)
=(1/2)log(5)(3)+log(5)(2)
=(1/2)*(a-b/2)+b/2
=a/2-b/4+b/2
=a/2+b/4

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