Решите уравнение 2^х+1 + 2^х+2 = 36

Решение

2^ (х+1) + 2^ (х+2) = 36

ОДЗ:

x + 1 > 0, x > - 1

x + 2 > 0, x > - 2

x ∈ ( - 1; + ∞)

2 * (2^x) + 2 ² * (2^x) = 36

6 * (2^x) = 36

2^x = 6

log₂ (2^x) = log₂ 6

x = log₂ 6

x = log₂ 2 + log₂ 3

x = 1 + log₂ 3