SOLUTION: solve for x. 2 log2 x - log2 (x+4)= log2 2

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Question 150019: solve for x.
2 log2 x - log2 (x+4)= log2 2
Found 2 solutions by stanbon, Fombitz:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
2 log2 x - log2 (x+4)= log2 2
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Keep the base in mind.
2 logx - log(x+4) = log2
logx^2 - log(x+4) = log2
log[x^2/(x+4)] = log2
x^2/(x+4) = 2
x^2-2x-8 = 0
(x-4)(x+2) = 0
x = 4 or x = -2
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x cannot be -2 as that would make the problem statement meaningless.
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Final solution: x = 4
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Cheers,
Stan H.

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Logarithm rules
log%28%28A%2AB%29%29=log%28A%29%2Blog%28B%29
log%28%28A%29%5EN%29=Nlog%28A%29
log%28%28A%2FB%29%29=log%28A%29-log%28B%29
.
.
.
2%2Alog%282%2Cx%29-log%282%2C%28x%2B4%29%29=log%282%2C2%29
log%282%2Cx%5E2%29-log%282%2C%28x%2B4%29%29=log%282%2C2%29
log%282%2C%28x%5E2%2F%28x%2B4%29%29%29=log%282%2C2%29
Take the inverse log of both sides.
x%5E2%2F%28x%2B4%29=2
x%5E2=2%28x%2B4%29
x%5E2=2x%2B8
x%5E2-2x-8=0
x-4%29%28x%2B2%29=0
First solution
x-4=0
x=4
Second solution
x%2B2=0
x=-2
Second solution is not allowed since log%282%2C%28-2%29%29 is not defined.
highlight%28x=4%29