SOLUTION: What is the solution of: Log2X + Log2(X-12)=6

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Question 1034578: What is the solution of: Log2X + Log2(X-12)=6
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Assume the problem is
log%282%2C%28X%29%29+%2B+log%282%2C%28X-12%29%29+=+6
adding logs is multiply so this is
log%282%2C%28X%28X-12%29%29%29+=+6
the exponent equiv of logs
X(X-12) = 2^6
distribute X
X^2 - 12X = 64
Forms a quadratic equation
X^2 - 12X - 64 = 0
Factors to
(X-16)(X+4) = 0
X = 16; only the positive solution can be used in the original problem
:
;
See if this checks out wit X=16
log%282%2C%2816%29%29+%2B+log%282%2C%2816-12%29%29+=+6
log%282%2C%2816%29%29+%2B+log%282%2C%284%29%29+=+6
16 is the 4th & 4 is the 2nd power of 2, therefore
4 + 2 = 6