lg2(lg5-lg2)-lg5(lg5+3lg2)等于

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lg2(lg5-lg2)-lg5(lg5+3lg2)等于
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lg2(lg5-lg2)-lg5(lg5+3lg2)等于
lg2(lg5-lg2)-lg5(lg5+3lg2)等于

lg2(lg5-lg2)-lg5(lg5+3lg2)等于
lg2(lg5-lg2)-lg5(lg5+3lg2)
=lg2lg5-(lg2)^2-(lg5)^2-3lg5lg2
=-[(lg2)^2+2lg2lg5+(lg5)^2]
=-(lg2+lg5)^2
=-[lg(2*5)]^2
=-1