Log₂(7 + 6x) = log₂(7 - 6x) + 2
ОДЗ
7+6х > 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