Решите уравнение log2 (7+6x) = log2 (7-6x) + 2

Log₂ (7 + 6x) = log₂ (7 - 6x) + 2

ОДЗ

7+6 х > 0; = > x > - 7/6;

7-6x > 0; = > x < 7/6;

- 7/6 < x < 7/6

Решение

log₂ (7 + 6x) = log₂ (7 - 6x) + log₂4

log₂ (7 + 6x) = log₂ ((7 - 6x) * 4)

(7 + 6x) = 4 * (7 - 6x)

7 + 6x = 28 - 24x

24x + 6x = 28 - 7

30x = 21

x = 21/30 = 7/10 = 0,7

х = 0,7 (удовлетворяет ОДЗ)

Проверка

log₂ (7 + 6*0,7) = log₂ (7 - 6*0,7) + 2

log₂ 11,2 = log₂ 2,8 + 2

log₂ 11,2 = log₂ 2,8 + iog₂4

log₂ 11,2 = log₂ (2,8 * 4)

log₂ 11,2 = log₂ 11,2

11,2 = 11,2

Ответ х = 0,7