SOLUTION: Solve the equation and check your solutions. List any extraneous answer. log(3x-13)=2-logx

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Solve the equation and check your solutions. List any extraneous answer. log(3x-13)=2-logx       Log On


   

Question 1031747: Solve the equation and check your solutions. List any extraneous answer.
log(3x-13)=2-logx
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
log(3x-13)=2-logx
<==> log%28%283x%5E2+-+13x%29%29+=+2 <==> 3x%5E2+-+13x+=+100
<==> 3x%5E2+-+13x+-+100+=+0 ==> (3x - 25)(x+4) = 0
==> x = -4 or x = 25/3.
Obviously x = -4 won't satisfy the original equation. (An extraneous solution!)
x=25/3 does satisfy the original equation , hence the solution.