Let `a >1` be a real number. Then the number of roots equation `a^(2(log)_2x)=15+4x^((log)_2a)` is 2 (b) infinite (c) 0 (d) 1

Options

A. 2
B. infinite
C. 0
D. 1

Answer

D

Explanation

Given equation can be written as
`(a^(log_(2)x))^(2)=5+4 a^(log_(2) x)`
Let `a^(log_(2)x)=t`.Then the given equation becomes
` r^(2) - 4t-5 = 0`
`rArr (t-5)(t+1) = 0`
` rArr t = 5 or t =- 1` (rejected)
` :. A^(log_(2)x) = 5`
` rArr x^(log_(2)a) = 5`
` rArr x = 5^(log_(a)2)`