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))
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)