Log(2) (x+5)- log(2) (x-1) > 1

Question

Log(2) (x+5)- log(2) (x-1) > 1

Answer 1

ОДЗ: x>-5, x>1. x∈(1;+∞)

log2((x+5)/(x-1))>1

log2((x+5)/(x-1))>log2(2)

(x+5)/(x-1)>2

(x+5-2x+2)/(x-1)>0

(7-x)/(x-1)>0

методом интервалов получаем ответ: x∈(1;7)