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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 PreCalc 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: 20,805 Thanks: 2150  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 nonzero. Multiply both sides by (x  2)². The graph of the resulting lefthand side is a parabola. 3. Multiply both sides by 2?(x² + 1), then square both sides of the resulting equation. 

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