2(log8 72+log9 72)=2log9 72×log8 72此式子如何理解..麻烦您写下过程..感谢...

2log9 72×log8 72
＝2（log9 8+1)*(log8 9 +1)
=2(1+log8 9+log9 8 +1)
=2(log8 8+log8 9+log9 8 +log 9 9 )
=2(log8 72+log9 72)

根据换底公式 log8 72=1/log72 8
原式=2(1/log72 8+1/log72 9) 通分有2((log72 8+log72 9)/log72 8*log72 9)=2/log72 9 *log72 8 然后再换回去就可以了

原式=2[(lg72/lg8)+(lg72/lg9)]
=2lg72(lg8+lg9)/(lg8lg9)
=2lg72lg72/(lg8lg9)
=2(lg72/lg8)*(lg72/lg9)
=2(log9 72)*(log8 72)