Let a > 1 be the real number . then the number of roots equation a2log2⁡x=5+4xlog2⁡a is

Given equation can be written as alog2⁡x2=5+4alog2⁡x Let alog2⁡x=t.  Then the given equation becomes t2−4t−5=0⇒(t−5)(t+1)=0⇒t=5 or t=−1 (rejected) ∴alog2⁡x=5⇒xlog2⁡a=5⇒x=5loga⁡2