SOLUTION: log2(x)+log2(x-3)=2

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Question 1139555: log2(x)+log2(x-3)=2
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39620) About Me  (Show Source):
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


log%282%2C%28x%29%29%2Blog%282%2C%28x-3%29%29+=+2

Rewrite the right side in terms of log base 2:

log%282%2C%28x%29%29%2Blog%282%2C%28x-3%29%29+=+log%282%2C4%29

Write the left side as a single logarithm using basic rules of logarithms:

log%282%2C%28x%28x-3%29%29%29+=+log%282%2C4%29

The logs are equal, so the arguments are equal:

x%28x-3%29+=+4
x%5E2-3x-4+=+0
%28x-4%29%28x%2B1%29+=+0

x+=+4 or x+=+-1

x=-1 does not work; the argument of a logarithm can't be negative.

x=4 works:

log%282%2C4%29%2Blog%282%2C%284-3%29%29+=+log%282%2C4%29%2Blog%282%2C1%29+=+2%2B0+=+2

ANSWER: x = 4