SOLUTION: ln(x-3)-ln(x+10)=ln(x-4)-ln(x+4)

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: ln(x-3)-ln(x+10)=ln(x-4)-ln(x+4)      Log On


   

Question 1057650: ln(x-3)-ln(x+10)=ln(x-4)-ln(x+4)
Answer by solve_for_x(190) About Me  (Show Source):
You can put this solution on YOUR website!
Using the following law of logarithms:

ln(a) - ln(b) = ln(a/b)

the equation can be rewritten as:

ln%28%28x-3%29%2F%28x%2B10%29%29+=+ln%28%28x+-+4%29%2F%28x+%2B+4%29%29

If ln(a) = ln(b), then a = b. Applying this to the above equation gives:

%28%28x-3%29%2F%28x%2B10%29%29+=+%28%28x+-+4%29%2F%28x+%2B+4%29%29

Multiplying both sides by (x + 10)(x + 4) then gives:
(x - 3)(x + 4) = (x - 4)(x + 10)

Using the FOIL method to expand the terms on both sides gives:

x^2 - 3x + 4x - 12 = x^2 - 4x + 10x - 40

x^2 + x - 12 = x^2 + 6x - 40

Subtracting x^2 from both sides leaves:

x - 12 = 6x - 40

6x - 40 = x - 12

Adding 40 to both sides gives:

6x = x - 12 + 40

6x = x + 28

Subtracting x from both sides then gives:

6x - x = 28

5x = 28

Dividing both sides by 5 then gives:

x = 28/5