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Question

If x=logabc,y=logb,z=logcab, then

A
1x+1+1y+1+1z+1=1
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B
1x1+1y1+1z1=1
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C
xyz=x+y+z+1
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D
xyz=1
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Solution

The correct option is A 1x+1+1y+1+1z+1=1
x=logabc1+logbcloga=x+1y=logbca1+logcalogb=y+11+logablogc=z+1loga+logbcloga=x+1logb+logcalogb=y+1logc+logablogc=z+1logabcloga=x+1logabclogb=y+1logabclogc=z+111+x+11+y+11+z=logalogabc+logblogabc+logclogabc11+x+11+y+11+z=loga+logb+logclogabc11+x+11+y+11+z=1

Hence, this is the answer.

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