Question

решите неравенство 11log13(x^2 -4x-5)<= 12+ log13((x+11)^11/x-5)

Answer 1

11log13(x^2 -4x-5)<= 12+ log13((x+1)^11/x-5) 

ОДЗ: (x^2 -4x-5)>0 (-беск;-1)U(5;беск)

 

11log13(x^2 -4x-5)=11log13((x+1)(x-5))=11log13(x+1)+11log13(x-5)

log13((x+1)^11/x-5)=11log13(x+1)-log13(x-5)

 

11log13(x+1)+11log13(x-5)<= 12+11log13(x+1)-log13(x-5)

12log13(x-5)<= 12

log13(x-5)<= 1 х>5

log13(x-5)<= log13(13)

(13-1)(13-x+5)>=0

18-x>=0

 

х (5;18]