Вычислите log₁/₂ (3/4) - log₁/₂ (3/2)

Согласно свойству логарифмов log a (b/c) = log a b - log a c.

По правилу деления дробей a/b : c/d = a/b * d/c = (a * d) / (b * c).

Тогда:

log 1/2 (3/4) - log 1/2 (3/2) = log 1/2 ((3/4) : (3/2)) = log 1/2 ((3/4) * (2/3)) = log 1/2 ((3 * 2) / (4 * 3)) = log 1/2 (2/4) = log 1/2 (1/2) = 1.