(1/log2 10) + (1/log5 10) =lg2 + lg5

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(1/log2 10) + (1/log5 10) =lg2 + lg5
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(1/log2 10) + (1/log5 10) =lg2 + lg5
(1/log2 10) + (1/log5 10) =lg2 + lg5

(1/log2 10) + (1/log5 10) =lg2 + lg5
用换底公式
loga N=logb N/logb a
所以1/log2 10=1/[(log10 10)/(log10 2)]=log10 2/log10 10=lg2/lg10=lg2
同理1/log5 10=lg5
所以(1/log2 10) + (1/log5 10) =lg2 + lg5

换底公式
log2 10=lg10/lg2 公式必须记住 书上的

(1/log2 10) + (1/log5 10)=1/(lg10/lg2)+1/(lg10/lg5)=lg2/lg10+lg5/lg10=lg2+lg5=lg10=1

log2 10等于lg10/lg2
log5 10等于lg10/lg5
所以原式等于lg2/lg10+lg5/lg10
而lg10=1
所以原式等于lg2+lg5