SOLUTION: log base 9 of (x-6) + log base 9 of (x+2) =1

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Question 256085: log base 9 of (x-6) + log base 9 of (x+2) =1
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
log base 9 of (x-6) + log base 9 of (x+2) =1
.
++++log%289%2C%28x-6%29%29+%2B+log%289%2C%28x%2B2%29%29+=1
.
Applying "log rules":
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++++log%289%2C%28x-6%29%28x%2B2%29%29+=1
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++++%28x-6%29%28x%2B2%29+=+9%5E1
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++++x%5E2%2B2x-6x-12+=+9
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++++x%5E2-4x-12+=+9
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++++x%5E2-4x-21+=+0
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++++%28x-7%29%28x%2B3%29+=+0
.
x = {7, -3}
But, plugging it back into the original equation shows that -3 is an "extraneous" solution -- throw it out. Leaving:
x = 7