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(log23+lOg427)(log34+log98)= 23中2是底数3是真数...

(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

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

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

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.

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

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

(2) log23●log34● log45● log52 =lg3/lg2*lg4/lg3*lg5/lg4*lg2/lg5 =1 (3)(log43+log83)(log32+log92) =(lg3/lg4+lg3/lg8)(lg2/lg3+lg2/lg9) =(lg3/2lg2+lg3/3lg2)(lg2/lg3+lg2/2lg3) =(lg3/lg2)(1/2+1/3)*(lg2/lg3)(1+1/2) =(1/2+1/3)(1+1/...

应用对数换底公式得到哦 log2 3•log3 4•log4 5•log5 6•log6 7•log7 8 =(lg3/lg2)×(lg4/lg3)×(lg5/lg4)×(lg6/lg5)×(lg7/lg6)×(lg8/lg7) =log2 8 =log2 2³ =3

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

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