SOLUTION: log base 2 of (x-5) - log base 2 of (x+2) = 3

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Question 599291: log base 2 of (x-5) - log base 2 of (x+2) = 3
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The key is to express +3+ as a log to the base +2+
+log%28+2%2C+x+%29+=+3+
+log%28+2%2C+8+%29+=+3+
+log%28+2%2C+x-5+%29+-+log%28+2%2C+x%2B2+%29+=+log%28+2%2C+8+%29+
Use the rule:
+log%28a%29+-+log%28b%29+=+log%28a%2Fb%29+
+log%28+2%2C+%28+x-5+%29%2F%28+x%2B2+%29+%29+=+log%28+2%2C8+%29+
+%28+x-5+%29+%2F+%28+x%2B2+%29+=+8+
+x+-+5+=+8%2A%28+x+%2B+2+%29+
+x+-+5+=+8x+%2B+16+
+7x+=+-21+
+x+=+-3+
check:
+log+%282%2C+%28x-5%29%29+-+log+%282%2C%28x%2B2%29+%29+=+3+
+log+%282%2C%28-8%29+%29+-+log+%282%2C%28-1%29+%29+=+3+
+log%28+2%2C+%28-8%29%2F%28-1%29+%29+=+3+
+log%28+2%2C8+%29+=+3+
OK