Question

решить уравнение
log2(x+4)-log2(x-11)=4

Answer 1

Решение неравенства на фото:

Answer 2

ОДЗ:
x+4 > 0
x > -4

x-11 > 0
x > 11

log2(x+4)-log2(x-11) = 4

log2((x+4) / (x-11)) = 4

2^4 = (x+4) / (x-11)

16(x-11) = x+4

16x -176 = x+4

16x -x = 4 + 176

15x = 180

x = 12, 12 > 11

Проверка:
log2(12+4)-log2(12-11) = 4

log2(16)-log2(1) = 4

4 - 0 = 4

4 = 4

Ответ: 12.