Log2 (x+1) - log4 x= 1

Log2 (x + 1) = 1 + log4 x.

Log2 (x + 1) = log4 4 + log4 x.

Log2 (x + 1) = log4 (4 * x).

Log2 (x + 1) = log2^2 (4 * x).

Log2 (x + 1) = ½ * log2 (4 * x).

2 * Log2 (x + 1) = log2 (4 * x).

Log2 (x + 1)^2 = log2 (4 * x).

Избавляемся от логарифмов с обеих сторон равенства.

(x + 1)^2 = 4 * x.

x^2 + 2 * x + 1 = 4 * x.

x^2 – 2 * x + 1 = 0.

(x – 1)^2 = 0.

x = 1.

Проверка:

Log2 (x + 1) – log4 x = 1.

Log2 (1 + 1) – log4 1 = 1.

Log2 2 – 0 = 1.

1 = 1.

Ответ: х = 1.