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I have got the answer of the question which satisfies the condition given, but its not actually the answer, the question is:- log(ax) - 2log(x+1) = 0 . What is the value of a for which the above equation has exactly 1 root? The answer which I got is 4. It satisfies the quadratic as well as log. But the teacher cut the whole marks. I dont know the answer, since it was the test paper of my friend and he had got no marks for getting 4. The question is of 8 marks, so it shouldnt be that easy. Please help me.

I have got the answer of the question which satisfies the condition given, but its not actually the answer, the question is:-


log(ax) - 2log(x+1) = 0 . What is the value of a for which the above equation has exactly 1 root?


The answer which I got is 4. It satisfies the quadratic as well as log. But the teacher cut the whole marks. I dont know the answer, since it was the test paper of my friend and he had got no marks for getting 4. The question is of 8 marks, so it shouldnt be that easy. Please help me.

Grade:12

1 Answers

Badiuddin askIITians.ismu Expert
148 Points
12 years ago

Dear avijit

given

log(ax) - 2log(x+1) = 0

for this

ax>0   and x+1>0

 

lets solve

 log(ax) - 2log(x+1) = 0

or ax= (x+1)2

or x2 + x(2-a) +1=0

for unique solution discrimnent must be zero

 which give a=0 or 4

but ax>0 so a can't be zero

for a=4   x=1 is solution

which satisfy the given equation

Please feel free to post as many doubts on our discussion forum as you can. If you find any question Difficult to understand - post it here and we will get you the answer and detailed solution very quickly.
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Regards,
Askiitians Experts
Badiuddin

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