Results 1 to 3 of 3

Math Help - Need help with a precalc question!

  1. #1
    Newbie
    Joined
    Jan 2009
    Posts
    6

    Need help with a precalc question!

    hey guys, i have a question that i need help on.
    it says use the "Rule of Four" to verbally, algebraicly, numerically, and graphically solve the problem.
    Find all teh real numbers such that: x^2log(sub 3)x<5xlog(sub 3)x

    anyone got any ideas to help me out with this?
    i tried applying the change of base formula, but i dont know where i am going with that. please help
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member AlvinCY's Avatar
    Joined
    Feb 2007
    From
    I live in Sydney, Australia.
    Posts
    69
    hey guys, i have a question that i need help on.
    it says use the "Rule of Four" to verbally, algebraicly, numerically, and graphically solve the problem.
    Find all teh real numbers such that: x^2log(sub 3)x<5xlog(sub 3)x

    Ok, I have NO IDEA what the rule of four is... but I do have a solution.

    x^2log_3 x<5xlog_3x

    There is a log_3 x on either side, so logically you would divide both sides by that, but when you do so, you have to consider the value of log_3 x very carefully, if log_3 x \ne0, then you're fine, dividing both sides by log_3 x gets you:

    x^2 < 5x
    x^2 - 5x < 0
    x(x-5) < 0

    When you plot the parabola x(x-5)=0, you can easily see that the solution for x(x-5) < 0 is 0<x<5

    Now, consider the case when log_3 x=0, this only occurs if x=1:

    When x=1, LHS = 0, RHS = 0, hence LHS is not less than RHS, which means if you solve x^2log_3 x<5xlog_3x, x=1 should NOT be a solution.

    So the solution to x^2log_3 x<5xlog_3x is 0<x<5, x\ne1.

    Hope that helps.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,830
    Thanks
    123
    Quote Originally Posted by robdarftw View Post
    hey guys, i have a question that i need help on.
    it says use the "Rule of Four" to verbally, algebraicly, numerically, and graphically solve the problem.
    Find all teh real numbers such that: x^2log(sub 3)x<5xlog(sub 3)x

    anyone got any ideas to help me out with this?
    i tried applying the change of base formula, but i dont know where i am going with that. please help
    1. Domain: D=(0,\infty) \setminus \{1\}

    2. Since \log_3(x) > 0 \ if\ x>1

    x^2 \log_3(x)<5x \log_3(x)~\implies~x^2<5x~\implies~x(x-5)<0. Therefore 1<x<5

    3. Since \log_3(x)<0\ if\ 0<x<1

    x^2 \log_3(x)<5x \log_3(x)~\implies~x^2>5x~\implies~x(x-5)>0. Therefore x>5

    4. By the way: The case x = 5 is excluded because you'll get an equation if x = 5
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. ln division question (precalc section?)
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: May 26th 2010, 06:38 AM
  2. precalc
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: February 22nd 2009, 10:17 AM
  3. Precalc Graphing/area trapazoid question
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: February 12th 2009, 04:56 PM
  4. Precalc question
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: January 20th 2009, 12:48 AM
  5. Precalc question
    Posted in the Pre-Calculus Forum
    Replies: 5
    Last Post: December 6th 2008, 08:10 PM

Search Tags


/mathhelpforum @mathhelpforum