急急急急 数学 求 （log3 2+log9 2）-（log4 3+log8 3）

答：
（log3 2+log9 2）-（log4 3+log8 3）
=log3(2)+log9(2)-log4(3)-log8(3)
=log3(2)+log3(2)/log3(9)-log3(3)/log3(4)-log3(3)/log3(8)
=log3(2)+(1/2)log3(2)-1/[2log3(2)]-1/[3log3(2)]
=(3/2)log3(2)-(5/6)/log3(2)

怀疑中间不是减号，而是乘号：
（log3 2+log9 2）×（log4 3+log8 3）
=[log3(2)+log9(2)]×[log4(3)+log8(3)]
=[log3(2)+log3(2)/log3(9)]×[log3(3)/log3(4)+og3(3)/log3(8)]
=[log3(2)+(1/2)log3(2)]×{1/[2log3(2)]+1/[3log3(2)]}
=[(3/2)log3(2)]×[(5/6)/log3(2)]
=5/4

=(lg2/lg3+lg2/lg9)-(lg3/lg4+lg3/lg8)
=(lg2/lg3+lg2/2lg3)-(lg3/2lg2+lg3/3lg2)
=3lg2/2lg3-5lg3/6lg2