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)`, thenA. 2B. infiniteC. 0D. 1

Let `agt1` be a real number . If S is the set of real number `x` that

1.	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)`, thenA. 2B. infiniteC. 0D. 1
Answer» Correct Answer - D 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)`