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September 7th, 2007, 06:28 AM   #1
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A few problems that I'm stuck on..

1. Simplify: ln (3x^2 - 9x) + ln (1 / 3x)
2. Solve for x: (x + 3) / (x - 2) > 0
3. Solve for x: Sqrt(x^2 + 1) - (x^2) / Sqrt(x^2 + 1) = 1/2

Help in solving these would be much appreciated. These are from a review sheet in my Calculus class covering Pre-Calc concepts and none of these are in the book. Thank you.
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September 7th, 2007, 07:39 AM   #2
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Re: A few problems that I'm stuck on..

For #1, remember that ln(xy) = ln(x) + ln(y).

For #2, solve as though an equality, then check a point on each side to see which way the inequality 'points'.
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September 7th, 2007, 07:59 AM   #3
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Re: A few problems that I'm stuck on..

Below are some hints which should make things easy for you.

1. Use the rule ln(A) + ln(B) = ln(AB) (where A > 0, B > 0).

2. Note that x is real and non-zero. Multiply both sides by (x - 2). The graph of the resulting left-hand side is a parabola.

3. Multiply both sides by 2?(x + 1), then square both sides of the resulting equation.
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