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Question

Find the value of 11+logba+logbc+11+logca+logcb+11+logab+logac.

A
2
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B
1
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C
0
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D
none of these
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Solution

The correct option is A 1
Now,
11+logba+logbc+11+logca+logcb+11+logab+logac
=1logbb+logba+logbc+1logcc+logca+logcb+1logaa+logab+logac
=1logbabc+1logcabc+1logaabc [ Using product rule of logarithtm]
=logblogabc+logclogabc+logalogabc
=logabclogabc
=1.

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