SOLUTION: This equation is on a work sheet that I need to solve: log (X+5) - log (X-1) = log (X+2) - log (X-3)

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: This equation is on a work sheet that I need to solve: log (X+5) - log (X-1) = log (X+2) - log (X-3)      Log On


   

Question 70983: This equation is on a work sheet that I need to solve:
log (X+5) - log (X-1) = log (X+2) - log (X-3)
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x:
Log%28x%2B5%29+-+Log%28x-1%29+=+Log%28x%2B2%29+-+Log%28x-3%29 Apply the quotient rule for logarithms to both sides.Log%28M%29-Log%28N%29+=+Log%28M%2FN%29
Log%28%28x%2B5%29%2F%28x-1%29%29+=+Log%28%28x%2B2%29%2F%28x-3%29%29 Applying the property: If M=N then Log%28M%29+=+Log%28N%29, so:
%28x%2B5%29%2F%28x-1%29+=+%28x%2B2%29%2F%28x-3%29 Simplify.
%28x-3%29%28x%2B5%29+=+%28x-1%29%28x%2B2%29 Perform the indicated multiplication.
x%5E2%2B2x-15+=+x%5E2%2Bx-2 Simplify.
2x-15+=+x-2 Subtract x from both sides.
x-15+=+-2 Add 15 to both sides.
x+=+13
Check: Substitute x=13
Log%2813%2B5%29+-+Log%2813-1%29+=+Log%2813%2B2%29+-+Log%2813-3%29
Log%2818%29+-+Log%2812%29+=+Log%2815%29+-+Log%2810%29
Log%2818%2F12%29+=+Log%2815%2F10%29
Log%283%2F2%29+=+Log%283%2F2%29