log2(x-2)+log2(x-3)=1

Question

log2(x-2)+log2(x-3)=1

Answer 1

log2(x-2)+log2(x-3)=1

ОДЗ x-3>0,=> x>3

log_2((x-2)(x-3)) = 1

log_2(x^2-5x+6) =1

x^2-5x+6 =2

x^2-5x+4 = 0

D = 25-16 = 9

x = (5-3)/2 = 1 (не входит в ОДЗ)

x = (5+3)/2 = 4

 Ответ:4