Question

Решите уравнение:lg(x-3)+lg(x-2)=1-lg5

Answer 1

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

lg(x-3)+lg(x-2)=lg10-lg5

lg(x-3)+lg(x-2)=lg2

lg(x-3)(x-2) = lg2

(x-3)(x-2) = 2

x² - 5x + 6 - 2 = 0

x² - 5x + 4 = 0

(x-4)(x-1) = 0

x = 4

x = 1

x>3

x>2

x = 4