Results 1 to 3 of 3

Math Help - How to solve this logarithmic inequality

  1. #1
    Newbie
    Joined
    Dec 2011
    Posts
    1

    How to solve this logarithmic inequality

    Hi all,
    How can I solve this?


    I tried with log_a (b) - log_a (c) = log_a (b/c) but the solution is (13+5x)/(x^2+5x+4)>=0 ...how is this possible?

    Thanks in advance
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,383
    Thanks
    1474
    Awards
    1

    Re: How to solve this logarithmic inequality

    Quote Originally Posted by LiberChronicon View Post
    Hi all,
    How can I solve this?

    I tried with log_a (b) - log_a (c) = log_a (b/c) but the solution is (13+5x)/(x^2+5x+4)>=0 ...how is this possible?
    You want to solve \frac{x^2-9}{x^2+5x+4)}\le 1.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    14,973
    Thanks
    1121

    Re: How to solve this logarithmic inequality

    Okay, as you say, log_{1/3}(x^2- 9)- log_{1/3}(x^2+ 5x+ 4)\ge 0 is the same as log_{1/3}\left(\frac{x^2- 9}{x^2+ 5x+ 4}\right)\ge 0.

    Further log_a(x)\ge 0, for any a< 1, if and only if x\le 1. That is, your inequality is the same as \frac{x^2- 9}{x^2+ 5x+ 4}\le 1.

    Subtracting 1 from both sides, \frac{x^2- 9}{x^2+ 5x+ 4}- 1= \frac{x^2- 9- (x^2+ 5x+ 4)}{x^2+ 5x+ 4}= \frac{-5x- 13}{x^2+ 5x+ 5}\le 0.

    Now, multiply both sides by -1.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Solving a logarithmic inequality.
    Posted in the Algebra Forum
    Replies: 3
    Last Post: September 30th 2011, 10:31 AM
  2. Logarithmic inequality
    Posted in the Algebra Forum
    Replies: 4
    Last Post: June 7th 2010, 10:59 AM
  3. Proving logarithmic inequality
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: April 12th 2010, 12:26 PM
  4. Logarithmic inequality?
    Posted in the Algebra Forum
    Replies: 1
    Last Post: April 29th 2009, 08:23 AM
  5. Logarithmic inequality
    Posted in the Algebra Forum
    Replies: 2
    Last Post: October 19th 2008, 07:26 AM

Search Tags


/mathhelpforum @mathhelpforum