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log23和log34

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

log23?log34?log45?…?log10231024=lg3lg2?lg4lg3?lg5lg4…lg1024lg1023=lg1024lg2=log21024log2210=10,故选C.

∵log23?log34?log4m=log327,∴lg3lg2?2lg2lg3?lgm2lg2=32lg3lg3,化为lgm=32lg2,∴m=22.故答案为:22.

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 .

由已知得a1?a2?a3?…?ak=lg(k+2)lg2=2 014,lg(k+2)=lg 22014,解得k=22014-2.故选:C.

由a1?a2??ak=lg3lg2?lg4lg3?lg5lg4??lg(k+2)lg(k+1)=lg(k+2)lg2=log2(k+2)=2008,解之得k=22008-2.答案:22008-2

由换底公式 log3 4=lg4/lg3 log4 8=lg8/lg4 log8 m=lgm/lg8 而log4 2=log4 (4)^(1/2)=1/2 由log3 4*log4 8*log8 m=log4 2 即lgm/lg3=1/2 即log3 m=1/2 m=3^(1/2)=根号3

(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.

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