Question

Помогите полжалуйста решить
lg(x-1)>0
log2(x+3)>1
log2(2-x)<2
log3(2x+1)<2

Answer 1

lg(x-1)>0  ⇒ $left { {{x-1>0} atop {x-1>1}} right.$⇒$left { {{x>1} atop {x>2}} right.$⇒x>2

log2(x+3)>1⇒$left { {{x+3>0} atop {x+3>2}} right.$⇒$left { {{x>-3} atop {x>-1}} right.$⇒x>-1

log2(2-x)<2 ⇒$left { {{2-x>0} atop {2-x<4}} right.$⇒$left { {{x<2} atop {x>-2}} right.$⇒ -2<x<2

log3(2x+1)<2⇒$left { {{2x+1>0} atop {2x+1<9}} right.$⇒$left { {{x>-1/2} atop {x<4}} right.$⇒ -1/2<x<4