SOLUTION: Solve for x: a) log base4 (x+2) + log base4 (n-4)=2 b) log base2 (x^2-2) - log base2 (1/2x+5)=1 Can someone please help me with these and show me how to check my answers ??????

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Question 127692: Solve for x:
a) log base4 (x+2) + log base4 (n-4)=2
b) log base2 (x^2-2) - log base2 (1/2x+5)=1 Can someone please help me with these and show me how to check my answers ??????
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Solve for x:
a) log base4 (x+2) + log base4 (x-4)=2
log base4 (x+2)(x-4) = 2
(x+2)(x-4) = 4^2
x^2-2x-24=0
Factor:
(x-6)(x+4)=0
Positive answer:
x = 6
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Checking:
log base4 (8) + log base4 (2) = 2
log base4 [8*2) = 2
4^2 = 16
====================
b) log base2 (x^2-2) - log base2 (1/2x+5 = 1
log base2 [(x^2-2)/((1/2)x+5)] = 1
[(x^2-2)/((1/2)x+5)] = 2
x^2-2 = x+10
x^2-x-12 = 0
(x-4)(x+3) = 0
Positive answer:
x = 4
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Checking:
log base2(14) - log base2 (7) = 1
log base2[14/7] = 1
14/7 = 2
2 = 2
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Cheers,
Stan H.