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Question

The value of logx+log(1+1x)+log(1+11+x)+log(1+12+x)++log(1+1(n1+x))

A
logxn
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B
lognx
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C
log(n+x)
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D
log(n1)x
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Solution

The correct option is C log(n+x)
logx+log(1+1x)+log(1+11+x)+log(1+12+x)++log(1+1(n1+x))

Multiplying first 2 terms and using property logn+logm=log(mn):
=log(x+1)+log(1+11+x)+log(1+12+x)++log(1+1(n1+x))

Multiplying first 2 terms again:
=log(x+2)+log(1+12+x)++log(1+1(n1+x))

Continuing this series we get:
=log(n1+x)+log(1+1(n1+x))
=log(n+x)

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