SOLUTION: log↓2(x-4)+log↓2(x)=5

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Question 1106348: log↓2(x-4)+log↓2(x)=5
Found 2 solutions by Alan3354, greenestamps:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
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Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


NOTE: you can write log base b of x as "log(b,x)". Or perhaps better, enclose the x in parentheses, as "log(b,(x))"

log%282%2C%28x-4%29%29%2Blog%282%2C%28x%29%29=5
log%282%2C%28x-4%29%29%2Blog%282%2C%28x%29%29+=+log%282%2C%2832%29%29 [rewrite the constant 5 as log base 2 of some number, so that all the terms in the equation are log base 2 of something]
log%282%2C%28%28x-4%29%28x%29%29%29+=+log%282%2C%2832%29%29 [sum of logs = log of the product]
log%282%2C%28x%5E2-4x%29%29+=+log%282%2C%2832%29%29 [algebra...]
x%5E2-4x+=+32 [if the logs of the expressions are equal, the expressions are equal]
x%5E2-4x-32+=+0
%28x-8%29%28x%2B4%29+=+0
x=8 or x=-4

But x=-4 does not satisfy the original equation (log of a negative number is undefined).
x=8 satisfies the original equation, so the unique solution to the equation is x=8.