Let `agt1` be a real number . If S is the set of real number `x` that are solutions to the equation `a^(2log_2x)=5+4x^(log_2a)`, then how many real number S contains?

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)`