Question 1057650
Using the following law of logarithms:


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


the equation can be rewritten as:


{{{ln((x-3)/(x+10)) = ln((x - 4)/(x + 4))}}}


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


{{{((x-3)/(x+10)) = ((x - 4)/(x + 4))}}}


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:


<strong>x = 28/5</strong>