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The number of real solution(s) of the eq...

The number of real solution(s) of the equation `9^(log_(3)(log_(e )x))=log_(e )x-(log_(e )x)^(2)+1` is equal to

A

0

B

1

C

2

D

3

Text Solution

Verified by Experts

The correct Answer is:
B
We have `9^(log_(3)(log_(e )x))=log_(e )x-(log_(e )x)^(2)+1`
`therefore gt 1`
The given equation `2(log_(e )x)^(2)-(log_(e )x)-1=0`
`therefore log_(e ),(1)/(sqrt(e ))` (not possible)
`rArr x = e`
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