SOLUTION: how do you solve the logarithmic equation log9(x-6)+log9(x-6)=1

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Question 685646: how do you solve the logarithmic equation log9(x-6)+log9(x-6)=1
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The trick is to make the substitution:
+1+=+log%28+9%2C9+%29+
++log%289%2C%28x-6%29%29+%2B+log%289%2C%28x-6%29%29+=+1+
++log%289%2C%28x-6%29%29+%2B+log%289%2C%28x-6%29%29+=+log%28+9%2C9+%29+
++log%289%2C%28x-6%29%5E2%29+=+log%28+9%2C9+%29+
+%28+x-6+%29%5E2+=+9+
+x%5E2+-+12x+%2B+36+=+9+
+x%5E2+-+12x+%2B+27+=+0+
+%28+x+-+3+%29%2A%28+x+-+9+%29+=+0+
+x+=+3+
+x+=+9+
---------
Only +x=9+ is valid. If you plug in
+x+=+3+, then
++log%289%2C%283-6%29%29+%2B+log%289%2C%283-6%29%29+=+1+
++log%289%2C+%28-3%29%29+%2B+log%289%2C+%28-3%29%29+=+1+
You can't have a log to a positive base
that gives you a negative number