计算:1/2lg(2x+2更号(x方-1)+lg(更号(x+1)-更号(x-1))(x>1)-学生作业帮-兵器谱
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计算:1/2lg(2x+2更号(x方-1)+lg(更号(x+1)-更号(x-1))(x>1)

来源:学生作业帮 编辑:作业帮 时间:2019/07/19 19:03:31

计算:1/2lg(2x+2更号(x方-1)+lg(更号(x+1)-更号(x-1))(x>1)

1/2lg(2x+2更号(x方-1)+lg(更号(x+1)-更号(x-1))(x>1)
=1/2lg[2x+2√(x^2-1)]+lg[√(x+1)-√(x-1)]
=1/2lg[(x+1)+2√(x^2-1)+(x-1)]+lg{2/[√(x+1)+√(x-1)]}
=1/2lg{[√(x+1)+√(x-1)]^2}+lg{2/[√(x+1)+√(x-1)]}
=lg[√(x+1)+√(x-1)]+lg{2/[√(x+1)+√(x-1)]}
=lg{[√(x+1)+√(x-1)]*2/[√(x+1)+√(x-1)]
=lg2

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