SOLUTION: log5(x+7)+log5(x-7)=2

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Question 685572: log5(x+7)+log5(x-7)=2
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The trick is to use +log%285%2C25%29+=+2+, then
+log%285%2C%28x%2B7%29%29+%2B+log%285%2C%28x-7%29%29+=+2+
+log%285%2C%28x%2B7%29%29+%2B+log%285%2C%28x-7%29%29+=+log%285%2C25%29+
+log%28+5%2C+%28x%2B7%29%2A%28x-7%29+%29+=+log%28+5%2C25+%29+
+log%28+5%2C+x%5E2+-+49+%29+=+log%28+5%2C25+%29+
+x%5E2+-+49+=+25+
+x%5E2+=+74+
+x+=+8.6023+
( There is a negative solution, too, but I can't use it
since that would give me log( 5, negative number ) ,
and there is no log to a positive base that can give
me a negative number.
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check answer:
+log%28+5%2C%288.6023%2B7%29%29+%2B+log%28+5%2C%288.6023-7%29%29+=+2+
+log%28+5%2C%28+15.6023+%29%29+%2B+log%28+5%2C%28+1.6023+%29%29+=+2+
+log%28+5%2C+24.9996+%29+=+2+
I think the error is due to rounding off