How do I solve this problem?

Question

Solve for x ln(x+5)=ln(x-9)-ln(x+9)

Answer 1

Ln(x+5)= ln(x-9)-ln(x+9) We can combine the logs on the right side so

ln(x+5)= ln (x-9/x+9). So that means

(x+5) = (x-9)/(x+9)

(x+5)(x+9)=x-9

x^2 +14x +45 =x-9

x^2 +13x +54=0 Will need to use quadratic equation to solve which I will leave to you . I can tell you that there are no real solutions to this since the discriminant of this equation (b^2 -4ac) is negative