求值:(log4(3)+log8(3))(log3(2)+log3(4))-log2(64)

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求值:(log4(3)+log8(3))(log3(2)+log3(4))-log2(64)求值:(log4(3)+log8(3))(log3(2)+log3(4))-log2(64)求值:(log4

求值:(log4(3)+log8(3))(log3(2)+log3(4))-log2(64)
求值:(log4(3)+log8(3))(log3(2)+log3(4))-log2(64)

求值:(log4(3)+log8(3))(log3(2)+log3(4))-log2(64)
换底公式
原式=(lg3/lg4+lg3/lg8)(lg2/lg3+lg4/lg3)-log2(2^6)
=(lg3/2lg2+lg3/3lg2)(lg2/lg3+2lg2/lg3)-log2(2^6)
=[(1/2+1/3)(lg3/lg2)][(1+2)(lg2/lg3)]-6log2(2)
约分
=(1/2+1/3)(1+2)-6
=5/2-6
=-7/2

1/2log2(3) 1/3log2(3))(log3(2) log3(4))-6log2(2)=5/2log2(3)log3(2)-6=5/2-6=-7/2