1.log2 3*log3 4*log4 5*log5 2 2.(log4 3+log8 3)8(log3 2+log9 2)

1、log2 3*log3 4*log4 5*log5 2
=lg2/lg3xlg3/lg4xlg4/lg5xlg5/lg2 （换底公式）
=1 （约分）

2.(log4 3+log8 3)*(log3 2+log9 2) 中间应为乘号
=(lg3/lg4+lg3/lg8)*(lg2/lg3+lg2/lg9)
=(lg3/2lg2+lg3/3lg2)*(lg2/lg3+lg2/2lg3)
=[(1/2+1/3)(lg3/lg2)]*[(1+1/2)(lg2/lg3)]
=(1/2+1/3)*(1+1/2)
=5/6*3/2
=5/4

答：换底公式等

1）
log2 3*log3 4*log4 5*log5 2
=log2(3)×log3(4)×log4(5)×log5(2)
=(lg3/lg2)×(lg4/lg3)×(lg5/lg4)×(lg2/lg5)
=1

2）
(log4 3+log8 3)*(log3 2+log9 2
=[ log4(3)+log8(3)] ×[log3(2)+log9(2)]
=[log2(3)/log2(4)+log2(3)/log2(8)]×(lg2/lg3+lg2/lg9)
=[ log2(3) ]×(1/2+1/3)×(lg2/lg3)×(1+1/2)
=(5/6)×(3/2)×[lg3/lg2]×(lg2/lg3)
=5/4