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.

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.
 We are all IITians and here to help you in your IIT JEE preparation.

 All the best.
 
Regards,
Askiitians Experts
Badiuddin