For which values?

Algebra Level 3

$\large \ln(23-x^2)>\ln(x^2 -9)$

Find the range of $x$ satisfying the inequality above.

{x>3, x<-3} {} {3<x<4, -4<x<-3} {-4<x<4} {2<x<4, -2<x<-1}

1 solution

Gabriel Miranda
May 2, 2016

For the inequality to be satisfied, (23-x²) must be greater than (x²-9). So we solve for x:

          23-x²>x²-9
          -2x²+32>0
         -4<x<4

But (x²-9) must be greater than 0, since ln(x²-9) is only defined for values greater than 0.

           x²-9>0
          x>3 or x<-3

Thus, the solution is {-4<x<-3, 3<x<4}