Question

Решите уравнение $log_{2}^{2} x+log_{2} frac{2}{x} = 3$

Answer 1

log²₂(x) + log₂(2) - log₂(x) - 3 = 0
log²₂(x) + 1 - log₂(x) - 3 = 0
log²₂(x)  - log₂(x) - 2 = 0
log₂(x) = t
t² - t - 2 = 0
D = 1 + 8 = 9
t = 2          или          t = - 1
log₂(x) = 2                log₂(x) = - 1
x = 4                        x = 1/2