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If $\log _{e}x+\log _{e}(1+x)=0,$ then:

  1. $x^{2}+x-1=0$
  2. $x^{2}+x+1=0$
  3. $x^{2}+x-e=0$
  4. $x^{2}+x+e=0$
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option (A)
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