2logx_корень из 3 - 1 = log_81 x^8.

2log_x√3 - 1 = log₈₁ x⁸,

2log_x3^1/2 - 1 = log (_{3 * 3 * 3 * 3)} x⁸,

2 * 1/2 * log_x3 - 1 = log (_{3 * 3 * 3 * 3)} x⁸,

log_x3 - 1 = 8 * log (₃ ) _⁴ x,

log_x3 - 1 = 8 * 1/4 * log ₃ x,

log_x3 - 1 = 2 * log ₃ x,

log_x3 - 1 = 2 / log _х 3, умножим обе части на log _х 3, получим:

log_x3 * log _х 3 - 1 * log _х 3 = 2 * log _х 3 / log _х 3,

(log_x3) ² - log _х 3 = 2,

log _х 3 = m,

m² - m - 2 = 0,

m₁ = - 1,

m₂ = 2,

log _х 3 = - 1,

х₁ ^{- 1} = 3,

х₁ = 3 ^-1,

х₁ = 1/3,

log _х 3 = 2,

х₂ ² = 3,

х₂ = √3,

Ответ: х₁ = 1/3, х₂ = √3.