SOLUTION: Solve the equation. 2 log2(x) − log2(x - 3) = 2 + log2(4)

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Question 537901: Solve the equation.
2 log2(x) − log2(x - 3) = 2 + log2(4)
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x:
2Log%5B2%5D%28x%29-Log%5B2%5D%28x-3%29+=+2%2BLog%5B2%5D%284%29 Apply the "power rule" to the first term on the left side.
Log%5B2%5D%28x%5E2%29-Log%5B2%5D%28x-3%29+=+2%2BLog%5B2%5D%284%29 Apply the "quotient rule" to the left side.
Log%5B2%5D%28x%5E2%2F%28x-3%29%29+=+2%2BLog%5B2%5D%284%29 Substitute Log%5B2%5D%284%29+=+2
Log%5B2%5D%28x%5E2%2F%28x-3%29%29+=+2%2B2
Log%5B2%5D%28x%5E2%2F%28x-3%29%29+=+4 Rewrite this in exponential form:
2%5E4+=+x%5E2%2F%28x-3%29 Substitute 2%5E4+=+16
16+=+x%5E2%2F%28x-3%29 Multiply both sides by %28x-3%29
16%28x-3%29+=+x%5E2 Simplify.
16x-48+=+x%5E2 Rewrite as:
x%5E2-16x%2B48+=+0 Solve by factoring.
%28x-4%29%28x-12%29+=+0 Apply the "zero product rule".
x-4+=+0 or x-12+=+0 therefore:
highlight%28x+=+4%29 or highlight_green%28x+=+12%29