Question

lg (x-3)+lg(x-2)=1-lg5

Answer 1

Решение
Lg (x-3)+lg(x-2)=1-lg5
ОДЗ: x - 3 > 0, x > 3
x - 2 > 0, x > 2
x ∈ (3 ; + ∞)
lg[(x - 3)*(x - 2)] = lg10 - lg5
lg[(x - 3)*(x - 2)] = lg10/5
lg[(x - 3)*(x - 2)] = lg2
(x - 3)*(x - 2) = 2
x² - 5x + 4 = 0
x₁ = 1 не удовлетворяет ОДЗ: x ∈ (3 ; + ∞)
x₂ = 4
Ответ: х = 4