SOLUTION: log3(2x-1) + log3(x-1) <1

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Question 759703: log3(2x-1) + log3(x-1) <1
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Make the conversion:
+1+=+log%28+3%2C+3+%29+
+log%28+3%2C+2x+-+1+%29+%2B+log%28+3%2C+x+-+1+%29+%3C+log%28+3%2C+3+%29+
+log%28+3%2C+%28+2x+-+1+%29%2A%28+x+-+1+%29%29+%3C+log%28+3%2C3+%29+
+%28+2x+-+1+%29%2A%28+x+-+1+%29+%3C+3+
+2x%5E2+-+x+-+2x+%2B+1++%3C+3+
+2x%5E2+-+3x+-+2+%3C+0+
Use quadratic formula
+x+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+2+
+b+=+-3+
+c+=+-2+
+x+=+%28-%28-3%29+%2B-+sqrt%28+%28-3%29%5E2+-+4%2A2%2A%28-2%29+%29%29+%2F+%282%2A2%29+
+x+=+%28+3+%2B-+sqrt%28+9+%2B+16+%29%29+%2F+4+
+x+=+%28+3+%2B-+sqrt%28+25+%29%29+%2F+4+
+x+=+%28+3+%2B+5%29+%2F+4+
+x+=+2+
and
+x+=+%28+3+-+5+%29+%2F+4+
+x+=+-1%2F2+
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+x+-+2+%3C+0+
+x+%3C+2+
and
+x+%2B+1%2F2+%3C+0+
+x+%3C+-1%2F2+
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+x+%3C+2+ is the answer since it covers both cases
Hope I got it