SOLUTION: Solve the logarithmic equation. be sure to reject the value of x that is not in the domain. What is the solution set?
ln (x-4) +ln (x+1) = ln (x-8)
thank you
Question 897542: Solve the logarithmic equation. be sure to reject the value of x that is not in the domain. What is the solution set?
ln (x-4) +ln (x+1) = ln (x-8)
thank you Answer by nerdybill(7384) (Show Source):
You can put this solution on YOUR website! ln (x-4) +ln (x+1) = ln (x-8)
ln (x-4)(x+1) = ln (x-8)
(x-4)(x+1) = (x-8)
x^2+x-4x-4 = x-8
x^2-3x-4 = x-8
x^2-3x+4 = x
x^2-4x+4 = 0
(x-2)(x-2) = 0
x = 2
but, if we substitute the above into the original equation we get:
ln (x-4) +ln (x+1) = ln (x-8)
ln (2-4) +ln (2+1) = ln (2-8)
ln (-2) +ln (x+1) = ln (-6)
since we can't take the ln of a negative we conclude that there is:
no solution
