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For x∈N, x>1 , and p=logxx+1 , q=logx+1x+2 then which one of the following is correct?

Correct Answer: p > q

Explanation:

k l > k + 1 l + 1  for (k,l) > 0 and  k > l 


 


 


 


Let     k = x+1    and   l = x


 


 


 


Therefore,  x + 1 x > ( x + 1 ) + 1 ( x ) + 1


 


 


 


 (x + 1) > x


 


 


 


Therefore,  log ( x + 1 ) log ( x ) > log ( x + 2 ) log ( x + 1 )


 


 


 


log x x + 1   > log x + 1 x + 2


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