Question

Решите уравнение с ОДЗ
log3(5x+1)log3x=4log(5x+1)

Answer 1

log3(5x+1)log3x=4log3(5x+1)

одз  5x + 1 > 0  x > -1/5

x > 0

x ∈ (0, +∞)

log3(5x+1)log3x - 4log3(5x+1) = 0

log3(5x+1)(log3x - 4) = 0

log3(5x+1) = 0

5x + 1 = 1

x = 0 нет по одз

log3x - 4 = 0

x = 3^4 = 81

ответ 81