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将下列指数式写成对数式:[√﹙lg²3-lg9+1﹚×﹙lg√27+lg8-lg1000﹚]/lg0.3×lg1.2
题目详情
将下列指数式写成对数式:[√﹙lg²3-lg9+1﹚×﹙lg√27+lg8-lg1000﹚]/lg0.3×lg1.2
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答案和解析
题目=[√﹙lg²3-2lg3+1﹚×﹙1.5lg3+3lg2-3﹚]/(lg3-lg10)×lg1.2
=√(lg3-1)²×1.5×﹙lg3+lg4-lg100﹚]/(lg3-lg10)×(lg12-lg10)
=(1-lg3)×1.5×﹙lg3+lg4-lg100﹚]/(lg3-1)×(lg12-lg10)
=-1.5×﹙lg3+lg4-lg100﹚]/(lg12-lg10)
=-1.5×﹙lg1.2-1﹚]/lg1.2
=-1.5+1.5/lg1.2
=1.5/lg1.2-1.5
=√(lg3-1)²×1.5×﹙lg3+lg4-lg100﹚]/(lg3-lg10)×(lg12-lg10)
=(1-lg3)×1.5×﹙lg3+lg4-lg100﹚]/(lg3-1)×(lg12-lg10)
=-1.5×﹙lg3+lg4-lg100﹚]/(lg12-lg10)
=-1.5×﹙lg1.2-1﹚]/lg1.2
=-1.5+1.5/lg1.2
=1.5/lg1.2-1.5
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