SOLUTION: find the solution(s) of the equation? log(x-1)-log(x+6)=log(x-2)-log(x-3)

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Question 236505: find the solution(s) of the equation?
log(x-1)-log(x+6)=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%28%28x-1%29%29-log%28%28x%2B6%29%29+=+log%28%28x-2%29%29-log%28%28x-3%29%29 Apply the quotient rule for logarithms:log%28%28M%29%29-log%28%28N%29%29+=+log%28%28M%2FN%29%29
log%28%28%28x-1%29%2F%28x%2B6%29%29%29+=+log%28%28%28x-2%29%2F%28x-3%29%29%29 If log%28%28M%29%29+=+log%28%28N%29%29 then M+=+N
%28x-1%29%2F%28x%2B6%29+=+%28x-2%29%2F%28x-3%29 Cross-multiply.
%28x-1%29%28x-3%29+=+%28x-2%29%28x%2B6%29 Perform the indicated multiplication.
x%5E2-4x%2B3+=+x%5E2%2B4x-12 Subtract x%5E2 from both sides.
-4x%2B3+=+4x-12 Add 4x to both sides.
3+=+8x-12 Add 12 to both sides.
15+=+8x Divide both sides by 8.
x+=+15%2F8
highlight%28x+=+1.875%29