Log2 (x-1) = log4 (x-1)

Log₂ (x-1) = log₄ (x-1)

Т. к. log₄ (x-1) = log₂² (x-1) = log₂ (x-1) / 2=0.5log₂ (x-1), то получаем:

log₂ (x-1) = log₄ (x-1) = 0.5log₂ (x-1) или log₂ (x-1) - 0.5log₂ (x-1) =

= 0.5log₂ (x-1) = 0, x-1=2⁰, x-1=1, x=2

Log (2, x-1) = log (4, x-1)

ОДЗ: x-1>0

log (2^2, (x-1) ^2) = log (4, x-1)

log (4, (x-1) ^2) = log (4. x-1)

Отсюда (x-1) ^2 = (x-1),

(x-1) (x-1-1) = 0

То есть

1) x-1=0 = > x=1. Корень не удовлетворяет ОДЗ: 1-1=0.

2) x-2=0 = > x=2. Удовлетворяет ОДЗ.

Ответ: 2.