SOLUTION: log ( 3 + x) - log (x - 5) = log 5

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Question 446144: log ( 3 + x) - log (x - 5) = log 5


Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Use the rule +log+%28a%29+-+log+%28b%29+=+log+%28a%2Fb%29+
+log+%28%283+%2B+x%29%29+-+log+%28%28x++-+5%29%29+=+log++5+
+log%28+%283%2Bx%29+%2F+%28x-5%29+%29+=+log%285%29+
Use the rule If +log%28a%29+=+log%28b%29+, then +a+=+b+
+%283%2Bx%29+%2F+%28x-5%29+=+5+
Multiply both sides by x-5
+x+%2B+3+=+5%2A%28+x+-+5+%29+
+x+%2B+3+=+5x+-+25+
+4x+=+28+
+x+=+7+
check answer:
+log+%28%283+%2B+x%29%29+-+log+%28%28x++-+5%29%29+=+log++5+
+log+%28%283+%2B+7%29%29+-+log+%28%287++-+5%29%29+=+log++5+
+log%2810%29+-+log%282%29+=+log%285%29+
+1+-+.30103+=+.69897+
+.69897+=+.69897+
OK