Математика ЕГЭ профиль 15 номер

(log4 16x)^2 * log16 (0,0625x)^2 =< log4 x/16 ---> ОДЗ: x > 0

___ log4 (16x) =
= log4 16 + log4 x =
= log4 4^2 + log4 x =
= 2*log4 4 + log4 x = 2 + log4 x

___ log16 (0,0625x)^2 =
= log(4^2) (0,0625x)^2 =
= 1/2 * 2 * log4 [(625 / 10000) * x] =
= log4 [(1/16) * x
= log4 (x/16)
=>
(2 + log4 x) * log4 (x/16) =< log4 (x/16)

(2 + log4 x) =< 1

log4 x >= 1

log4 x >= log4 4

x >= 4