SOLUTION: log3(3x+6)-log3(x-6)=2

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Question 206259: log3(3x+6)-log3(x-6)=2
Found 2 solutions by Marth, nerdybill:
Answer by Marth(57) About Me  (Show Source):
You can put this solution on YOUR website!
Remember that log%28a%29-log%28b%29=log%28a%2Fb%29
So given log3%283x%2B6%29-log3%28x-6%29=2
Simplify into log3%28%283x%2B6%29%2F%28x-6%29%29=2
2=log3%289%29
So, log3%28%283x%2B6%29%2F%28x-6%29%29=log3%289%29
Now you can remove the logarithms on both sides.
%28%283x%2B6%29%2F%28x-6%29%29=9
3x%2B6=9%28x-6%29
3x%2B6=9x-54
60=6x
x=10

Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
Applying log rules:
log3(3x+6)-log3(x-6)=2
log3[(3x+6)/(x-6)]=2
(3x+6)/(x-6) = 3^2
(3x+6)/(x-6) = 9
(3x+6) = 9(x-6)
3x+6 = 9x-54
6 = 6x-54
60 = 6x
10 = x