Question

log₃ ( x² - x - 2 ) ≤ 1 + log₃ $frac{x+1}{x+2}$ прошу, решите подробно! :)

Answer 1

log₃ ( x² - x - 2 ) ≤ 1 + log₃ 

x² - x - 2=(x-2)(x+1)

log₃ ( x² - x - 2 )=log₃(x+1)+log₃(x-2)

log₃ =log₃(x+1)-log₃(x+2)

log₃(x+1)+log₃(x-2)<=log₃(x+1)-log₃(x+2)+1

log₃(x-2)+log₃(x+2)<= log₃3

x^2-4<=3

x^2<=7   -sqrt(7)<=x<=sqrt(7)

x² - x - 2>0  x<-1 U x>2

 

-sqrt(7)<=x<-1 U (2;sqrt7]

 

(x+1)/(x+2)>0 x<-2 U x>-1

 

[-sqrt(7);-2) U (2;sqrt(7)]