Question

помогите доделать срочняк

Answer 1

x^(log(2)(x^3) - log(2)(x)^2 -3) = 1/x

x > 0 - ОДЗ

log(2)(x^3) - log(2)(x)^2 -3 = - 1

3*log(2)(x) - log(2)(x)^2 - 2 = 0

log(2)(x) = t

t^2 - 3*t + 2 = 0
t1 + t2 = 3
t1 * t2 = 2

t1 = 2, t2 = 1

log(2)(x)  = 2

x = 2^2 = 4

log(2)(x)  =1

x = 2^1 = 2

Оба решения удовлетворяют ОДЗ.

Ответ: x = 2, x = 4