Question

Решите уравнения
1. log16(5x-14)=0
2. log7(5-x)= log7(29-9x)
3. 2log2/25x + log25 x-1=0

Answer 1

Ответ:

Объяснение:

log16(5x-14) = 0

5x-14 = 16^0 = 1

5x = 15

x = 3

log7(5-x) = log7(29-9x)

5-x = 29-9x

8x = 24

x = 3

2log²25(x) + log25(x) - 1 = 0

Пусть, t = log25(x)

2t² + t - 1 = 0

D = 1+8 = 9

t1 = (-1+3)/4 = 0.5 ⇒ x = 25^(0.5) = √25 = 5

t2 = (-1-3)/4 = -1 ⇒ x = 25^(-1) = 1/25