SOLUTION: How would you work this problem out? Log base2x+ log base2(x-6)=4

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Question 292991: How would you work this problem out?
Log base2x+ log base2(x-6)=4
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
log%282%2C%28x%29%29%2Blog%282%2C%28x-6%29%29=4
log%282%2C%28x%28x-6%29%29%29=4
x%28x-6%29=2%5E4=16
x%5E2-6x-16=0
Factor,
%28x-8%29%28x%2B2%29=0
Two solutions:
x-8=0
x=8
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x%2B2=0
x=-2
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Verify the solutions.
log%282%2C%28x%29%29%2Blog%282%2C%28x-6%29%29=4
log%282%2C%288%29%29%2Blog%282%2C%288-6%29%29=4
3%2Blog%282%2C%282%29%29=4
3%2B1=4
4=4
True, it's a good solution.
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log%282%2C%28-2%29%29%2Blog%282%2C%28-2-6%29%29=4
log%282%2C%28-2%29%29%2Blog%282%2C%28-8%29%29=4
Log arguments must be positive.
This solution is not valid.
Only one solution, highlight_green%28x=8%29