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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.
Dear avijit
given
log(ax) - 2log(x+1) = 0
for this
ax>0 and x+1>0
lets solve
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
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