SOLUTION: Solve the equation In(x+5) -In(3) =In(x-3). Please show me how to break this down to where it would understand by a dummy like me. Thanks to anyone who can help

Algebra ->  College  -> Linear Algebra -> SOLUTION: Solve the equation In(x+5) -In(3) =In(x-3). Please show me how to break this down to where it would understand by a dummy like me. Thanks to anyone who can help      Log On


   

Question 72626: Solve the equation In(x+5) -In(3) =In(x-3).
Please show me how to break this down to where it would understand by a dummy like me.
Thanks to anyone who can help
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x:
ln%28x%2B5%29+-+ln%283%29+=+ln%28x-3%29
Rewrite the left side using the quotient rule of logarithms:ln%28M%29-ln%28N%29+=+ln%28M%2FN%29
ln%28%28x%2B5%29%2F3%29+=+ln%28x-3%29 Now apply the identity rule: If ln%28M%29+=+ln%28N%29 then M+=+N
%28x%2B5%29%2F3+=+x-3 Simplify and solve for x. Multiply both sides by 3.
x%2B5+=+3%28x-3%29
x%2B5+=+3x-9 Subtract x from both sides.
5+=+2x-9 Add 9 to both sides.
14+=+2x Divide both sides by 2.
7+=+x or x+=+7