【根号(lg的平方3-lg9+1)*(lg根号27+lg8-lg根号1000)】/(lg0.3)*(lg1.2)
问题描述：
【根号(lg的平方3-lg9+1)*(lg根号27+lg8-lg根号1000)】/(lg0.3)*(lg1.2)
答
【根号(lg的平方3-lg9+1)*(lg根号27+lg8-lg根号1000)】/(lg0.3)*(lg1.2)
={根号(lg²3-lg3²+1)*[(1/2)*lg3³+lg2³-(1/2)*lg10³]}/[lg(3/10)*lg(12/10)]
={根号(lg²3-2lg3+1)*[(3/2)(lg3)+3*lg2-(3/2)*lg10]}/[lg(3/10)*lg(12/10)]
={根号(1-lg3)²*[(3/2)(lg3)+3lg2-(3/2)*1]}/[(lg3-lg10)*(lg12-lg10)],[1-lg3>0]
={(1-lg3)*(3/2)[lg3+2lg2-1]}/[(lg3-1)*(lg12-1)]
=-(3/2)[lg3+lg4-1]/(lg12-1)
=-(3/2)[lg3*4-1]/(lg12-1)
=-(3/2)[lg12-1]/(lg12-1)
=-3/2