3log27 (3 х-2) = 727-основание

3 log ₂₇ (3 х - 2) = 7,

log _{27 ^1/3} (3 х - 2) = 7,

log _{(3 * 3 * 3) ^1/3} (3 х - 2) = 7,

log ₃ (3 х - 2) = 7,

log ₃ (3 х - 2) = log ₃ 3⁷,

(3 х - 2) = 3⁷,

3 х - 2 = 3⁷,

3 х = 3⁷ + 2,

х = (3⁷ + 2) / 3,

х = 3⁷/3 + 2/3,

х = 3 ^{(7 - 1)} + 2/3,

х = 3 ⁶ + 2/3,

х = 3 * 3 * 3 * 3 * 3 * 3 + 2/3,

х = 27 * 27 + 2/3,

х = 729 + 2/3,

х = 729 ²/₃.

Ответ: х = 729 ²/₃.