Results 1 to 6 of 6

Math Help - Log Function Restrictions

  1. #1
    Senior Member
    Joined
    Nov 2008
    Posts
    425

    Log Function Restrictions

    Hi there
    I need help with the restrictions on the variables of this question:

    Simplify. State any restrictions on the variables.

    log(x^2+7x+12)/log(x^2-9)

    So my answer is: log(x+4/x-3) which is correct.

    Now for the restrictions, I have:
    x<-4 and x>3

    However the back of the book says the answer is only x>3 and not x<-4 for the restrictions of the variables. But when I sub in any number such as -5 into the ORIGINAL log equation, i get a defined and positive log of x value. So? is mine correct or theirs? Explain fully.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,957
    Thanks
    1780
    Awards
    1
    Quote Originally Posted by skeske1234 View Post
    Simplify. State any restrictions on the variables.
    log(x^2+7x+12)/log(x^2-9)

    So my answer is: log(x+4/x-3) which is correct.

    Now for the restrictions, I have:
    x<-4 and x>3
    .
    The answer in red is not correct. The logarithm function does not work that way.
    [Math]\log \left( {x^2 + 7x + 12} \right) = \log \left( {x + 3} \right) + \log \left( {x + 4} \right)~\&~\log \left( {x^2 - 9} \right) = \log \left( {x + 3} \right) + \log \left( {x - 3} \right)[/tex].

    So the way you have written it does not allow the factors to divide out.

    But the restriction above in blue is the domain of the problem as you have written it.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor Amer's Avatar
    Joined
    May 2009
    From
    Jordan
    Posts
    1,093
    your question

    log\left(\frac{x^2+7x+12}{x^2-9}\right)

    or

    \frac{log(x^2+7x+12)}{log(x^2-9)}
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member
    Joined
    Nov 2008
    Posts
    425
    Sorry the question is:

    log[(x^2+7x+12)/x^2-9)]
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,957
    Thanks
    1780
    Awards
    1
    Quote Originally Posted by skeske1234 View Post
    Sorry the question is:
    log[(x^2+7x+12)/x^2-9)]
    In that case the donain is (-\infty , -4) \cup (3, \infty).
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor Amer's Avatar
    Joined
    May 2009
    From
    Jordan
    Posts
    1,093
    Quote Originally Posted by skeske1234 View Post
    Sorry the question is:

    log[(x^2+7x+12)/x^2-9)]

    your solution is correct

    \frac{x+4}{x-3} > 0

    x<-4 and x>3
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: June 28th 2010, 01:19 PM
  2. Replies: 1
    Last Post: June 12th 2010, 10:58 AM
  3. Restrictions for Max./Min. Problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: September 5th 2009, 01:43 AM
  4. restrictions
    Posted in the Algebra Forum
    Replies: 2
    Last Post: December 4th 2008, 11:11 AM
  5. restrictions for x
    Posted in the Algebra Forum
    Replies: 2
    Last Post: July 27th 2008, 01:33 PM

Search Tags


/mathhelpforum @mathhelpforum