Question

Помогите пж!
(2/log2x) + (5/log2x^2-log2x^3) = log2x/log2(x/8)

Ответ:(0;1) {2} (8;+∞)

Answer 1

log 2 (x) = t

2/t + 5/(2t - 3t) = t/t - 3

2/t - 5/t = t/t-3

-3/t = t/t-3

3/t = t/3-t

t^2 = 9 - 3t

t^2 + 3t - 9 = 0

D = 9 + 36 = 45

t = -3 + 3sqrt(5)/2

t = -3 - 3sqrt(5)/2

log 2 (x) = -3 + 3sqrt(5)/2

log 2 (x) = -3 - 3sqrt(5)/2

x = 2^(-3 + 3sqrt(5)/2)

x = 2^(-3 - 3sqrt(5)/2)

Ответ : 2^(-3 + 3sqrt(5)/2) ; 2^(-3 - 3sqrt(5)/2)