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

通分 lg3/lg2=2lg3/2lg2 ∴lg3/lg2+3lg3/2lg2 =(2lg3+3lg3)/2lg2 =5lg3/lg2 同理,2lg2/lg3=4lg2/2lg3 ∴2lg2/lg3+3lg2/2lg3 =(4lg2+3lg2)/2lg3 =7lg2/2lg3 再继续运算就可以了 谢谢~_~

(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

(1)log23?log34+lg4+lg25=lg3lg2?lg4lg3+2lg2+2lg5=lg4lg2+2(lg2+lg5)=2lg2lg2+2lg10=2+2=4;(2)m?3m?4m(6m)5?m14=m12?m13?m14m56?m14=m12+13+14m56+14=m1312m1312=1.

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

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×…×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.

1、 答案为1 2、 (log43+log83)(log32+log92) =( lg3/lg4 + lg3/ lg8 )( lg2/ lg3 + lg2/ lg9 ) =( lg3/ 2lg2 + lg3 /3lg2 )( lg2/ lg3 + lg2 /2lg3 ) = 1 /2 + 1/ 4 + 1/ 3 + 1/ 6 = 5/ 4 .

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

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