SOLUTION: Please help! Find the exact value for the solution of the equation. Simplify the radical. log((x^2+4))-log((x+2))=3+log((x-2))

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Please help! Find the exact value for the solution of the equation. Simplify the radical. log((x^2+4))-log((x+2))=3+log((x-2))      Log On


   

Question 386877: Please help! Find the exact value for the solution of the equation. Simplify the radical.
log((x^2+4))-log((x+2))=3+log((x-2))
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
log%28%28x%5E2+%2B+4%29%29-log%28%28x%2B2%29%29+=+log10%5E3+%2B+log%28%28x-2%29%29;
log%28%28x%5E2+%2B+4%29%2F%28x%2B2%29%29+=+log%2810%5E3%28x-2%29%29;
%28x%5E2+%2B+4%29%2F%28x%2B2%29+=+10%5E3%28x+-2%29;
x%5E2+%2B+4+=+10%5E3%28x%5E2+-+4%29;
x%5E2+%2B+4+=+10%5E3x%5E2+-+4%2A10%5E3;
4%2810%5E3+%2B+1%29+=+%2810%5E3+-+1%29x%5E2;
x%5E2+=+%284%2810%5E3+%2B+1%29%29%2F%2810%5E3+-+1%29;
x++=+2sqrt%28%284%2810%5E3+%2B+1%29%29%2F%2810%5E3+-+1%29%29. (The negative value of x has been eliminated, it won't satisfy the original equation.)