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log23?log34?log45?log52=______

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

解log3(4)×log4(5) =lg4/lg3×lg5/lg4 =lg5/lg3 =lg3(5)

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

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

(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/...

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