Question

Решите уравнение:
2log3x/log3(4x-3)=1

Answer 1

2log3x/log3(4x-3)=1

одх x > 0

4x - 3 > 0   x > 3/4

4x - 3 ≠ 1    x ≠ 1

x ∈ (3/4, 1) U (1, +∞)

2log3x = log3(4x-3)

log3x² = log3(4x-3)

x² = 4x-3

x² - 4x + 3 = 0

D =16 - 12 = 4

x12 = (4 +- 2)/2 = 1    3

x1 = 1 нет по одз

x2 = 3

ответ 3