SOLUTION: Solve for x: log 2,(x+6) + log 2,(x-1) = 3 Thank you for your help!

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Question 354511: Solve for x:
log 2,(x+6) + log 2,(x-1) = 3
Thank you for your help!
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
log 2,(x+6) + log 2,(x-1) = 3
log 2,(x+6)(x-1) = 3
log 2,%28x%5E2%2B5x-6%29 = 3. This is the same as
x%5E2%2B5x-6+=+2%5E3,
x%5E2%2B5x-6+=+8,
x%5E2%2B5x-14+=+0,
%28x%2B7%29%28x-2%29+=+0.
This gives x+=+-7 or x+=+2. The first value won't satisfy the original equation, so the final answer is x+=2.