My Math Forum A few problems that I'm stuck on..

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 September 7th, 2007, 06:28 AM #1 Newbie   Joined: Sep 2007 Posts: 1 Thanks: 0 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.
 September 7th, 2007, 07:39 AM #2 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms 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'.
 September 7th, 2007, 07:59 AM #3 Global Moderator   Joined: Dec 2006 Posts: 21,038 Thanks: 2274 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)². The graph of the resulting left-hand side is a parabola. 3. Multiply both sides by 2?(x² + 1), then square both sides of the resulting equation.

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