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计算:2723%2log23×log218+log23×log34=______

2723-2log23×log218+log23×log34=9-3×(-3)+lg3lg2×lg4lg3=9+9+2=20.故答案为:20.

解:log(2)3×log(3)4 =log(2)3×log(2)4/log(2)3 =log(2)4 =log(2)2² =2log(2)2 =2

(1)(2764)?13+(214)12+12log26=(6427)13+(94)12+12log26=43+32+16=3(2)(log23+log89)?(log34+log98+log32)=(log23+23log23)?(2log32+ 32log32+log32)=53log23?92log32=152

原式=lg3lg2?2lg2lg3+lg2(lg2+lg5)+lg5=2+lg2+lg5=2+1=3.故答案为:3.

log23×log34×log45×…×log1516=lg3lg2×lg4lg3×lg5lg4×…×lg16lg15=lg16lg2=log216=4.故答案为:4.

(18)?23+(log29)(log34)=382+(2log23)(2log32)=4+4=8.故答案为8.

log23?log34?log45?log52=lg3?lg4?lg5?lg2lg2?lg3?lg4?lg5=1.故答案为:1.

(1)原式=lg3lg2×2lg2lg3+32×23=2+72=74.(2)原式=log62(log62+2log63)+(log63)2=(log62)2+2log62?log63+(log63)2=(log62+log63)2=1.

:(log23)(log34)=lg3lg2?lg4lg3=lg4lg2=2.故答案为2.

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