Question

решить неравенство log2 (x-1)+log2(x-3)<3

Answer 1

log2 (x-1)+log2(x-3)<3

log2(x-1)*(x-3)<3

log2(x-1)*(x-3)<log2(8)

(x-1)*(x-3)-3<0

x-1 >0

x-3 > 0 вот и система неравенств!

x² - 4x + 3 - 3 < 0

x(x-4) < 0     (0;4)

х > 1

x > 3

ответ: (3;4)