log3(4) 即以2为底3的对数大于以3为底4的对数.这是高考前复习的一个数学题,当时做不出来,十年后用几种办法做出,当时难倒了多少数学高手.解法：log2(3) = lg3/lg2 = lg27/lg8 ；log3(4) = lg4/lg3 = lg16/lg9 ；因为, 1 ,所以, log3(4) .解法：log(2)3=lg3/lg2 log(3)4=lg4/lg
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log2(3)-log3(4)
=log2(3)-2log3(2)
=log2(3)-2/log2(3)
=[(log2(3))^2-2]/log2(3)
=[(log2(3))^2-2log2(2)]/log2(3)
=[(log2(3))^2-log2(4)]/log2(3)
=(log2(3)+log2(4))(log2(3)-log2(4))/log2(3)
∵log2(3)-log2(4)0 log2(3)>0∴log2(3)-log3(4)