Log₂x>0
log₂(log₂x)² - log₂(log₂(2^(3/2)x)) = 1
log₂ ((log₂x)² /(log₂(2^(3/2)x) ) = 1
(log₂x)² /(log₂(2^(3/2)x) = 2
(log₂x)² - 2(log₂(2^(3/2)) + log₂x) = 0
(log₂x)² - 2·(3/2) - 2log₂x = 0
(log₂x)² - 2log₂x - 3= 0
log₂x = t
t² -2t - 3 = 0
t = 3 или t = -1
log₂x = 3 log₂x = -1 - не входит в область определения
x = 2³ = 8