Question

Решите пример подробно, пожалуйста. (тут 2 корня)

Answer 1

x^(log(2) x) * 14^(log(2) 7) = x^(log(2) 7) * x^(log(2) 14)

ОДЗ  x > 0

log (xy) = log x + log y

логарифмируем по основанию 2

log(2) (x^(log(2) x) * 14^(log(2) 7)) = log(2) (x^(log(2) 7) * x^(log(2) 14))

log(2) x^(log(2) x) + log(2) 14^(log(2) 7) = log(2) x^(log(2) 7) + log(2)(x^(log(2) 14)

(log(2) x )*(log(2) x) + (log(2) 14)* (log(2) 7) = log(2) x * (log(2) 7) + (log(2) x)*(log(2) 14)

log(2) x = t

t²  - (log(2) 7 + log(2) 14)* t + log(2) 14 * log(2) 7 = 0

D =  (log(2) 7 + log(2) 14)²- 4*log(2) 14 * log(2) 7 = (log(2) 14 - log(2) 7)²

t12 = [ (log(2) 14 + log(2) 7) +-  (log(2) 14 - log(2) 7)]/2 = log(2) 14   и log(2) 7

1. log(2) x = log(2) 7

x = 7

2. log(2) x = log(2) 14

x = 14

ответ 7 и 14