证明不等式1/(log5(19))+(2/log3(19))+(3/log2(19))
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证明不等式1/(log5(19))+(2/log3(19))+(3/log2(19))
证明不等式1/(log5(19))+(2/log3(19))+(3/log2(19))<2
证明不等式1/(log5(19))+(2/log3(19))+(3/log2(19))
1/(log5(19))+(2/log3(19))+(3/log2(19))
=log19(5)+2*log19(3)+3*log19(2)
=log19(5*9*8)=log19(360)
这一题用到倒数原理:
1/[logb(a)]=loga(b) 该公式可用换底公式logb(a)=lga/lgb证明
于是原式=log19(360)
不等试左边=log19(5)+log19(9)+log19(8)=log19(360)