Results 1 to 8 of 8
Like Tree1Thanks
  • 1 Post By ILikeSerena

Math Help - solution set of the logarithm inequality

  1. #1
    rcs
    rcs is offline
    Senior Member rcs's Avatar
    Joined
    Jul 2010
    From
    iligan city. Philippines
    Posts
    455
    Thanks
    2

    solution set of the logarithm inequality

    Solution set: Log base 1/3 (x^2+ 4x +3) < = -1

    attempt:
    x^2 + 4x + 3 <= (1/3)^-1
    x^2 + 4x + 3 < = 3
    x^2 + 4x < = 0
    x ( x + 4) < = 0
    x < = 0, x < = -4


    i wonder why from the book i have read, the solution set is I.N. (-4, 0) or - 4 < x < 0

    please guide me on this problem

    thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Jun 2009
    Posts
    660
    Thanks
    133

    Re: solution set of the logarithm inequality

    At the point where you have x(x+4)<=0, sketch the graph of y = x(x+4).
    The range of values for which y<=0 should be obvious.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member ILikeSerena's Avatar
    Joined
    Dec 2011
    Posts
    733
    Thanks
    121

    Re: solution set of the logarithm inequality

    Hi rcs!

    Quote Originally Posted by rcs View Post
    Solution set: Log base 1/3 (x^2+ 4x +3) < = -1

    attempt:
    x^2 + 4x + 3 <= (1/3)^-1
    This is incorrect.
    When the base of the log is between 0 and 1 the inequality swaps around.

    x^2 + 4x + 3 < = 3
    x^2 + 4x < = 0
    x ( x + 4) < = 0
    x < = 0, x < = -4
    The last step is incorrect.
    If x would be smaller than -4, say -5, then both factors are negative, resulting in a positive number.
    Note that a product is negative, if and only if the factors have opposite signs.

    i wonder why from the book i have read, the solution set is I.N. (-4, 0) or - 4 < x < 0

    please guide me on this problem

    thanks
    Btw, are you aware that you cannot take the log of zero or a negative number?
    That is, you have the additional constraint that x^2+ 4x +3 > 0.
    It means that when you have solved your inequality, you need to verify that this constraint is satisfied.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    rcs
    rcs is offline
    Senior Member rcs's Avatar
    Joined
    Jul 2010
    From
    iligan city. Philippines
    Posts
    455
    Thanks
    2

    Re: solution set of the logarithm inequality

    Quote Originally Posted by ILikeSerena View Post
    Hi rcs!



    This is incorrect.
    When the base of the log is between 0 and 1 the inequality swaps around.



    The last step is incorrect.
    If x would be smaller than -4, say -5, then both factors are negative, resulting in a positive number.
    Note that a product is negative, if and only if the factors have opposite signs.



    Btw, are you aware that you cannot take the log of zero or a negative number?
    That is, you have the additional constraint that x^2+ 4x +3 > 0.
    It means that when you have solved your inequality, you need to verify that this constraint is satisfied.
    so if you were to solve it

    how would it be done?

    can you show it to me please...
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member ILikeSerena's Avatar
    Joined
    Dec 2011
    Posts
    733
    Thanks
    121

    Re: solution set of the logarithm inequality

    Ah, well, I don't like giving full solutions.
    But perhaps you can redo the calculation taking my remarks into account?
    Thanks from skeeter
    Follow Math Help Forum on Facebook and Google+

  6. #6
    rcs
    rcs is offline
    Senior Member rcs's Avatar
    Joined
    Jul 2010
    From
    iligan city. Philippines
    Posts
    455
    Thanks
    2

    Re: solution set of the logarithm inequality

    Quote Originally Posted by ILikeSerena View Post
    Ah, well, I don't like giving full solutions.
    But perhaps you can redo the calculation taking my remarks into account?
    if i would redo it how does the equation look like?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    rcs
    rcs is offline
    Senior Member rcs's Avatar
    Joined
    Jul 2010
    From
    iligan city. Philippines
    Posts
    455
    Thanks
    2

    Re: solution set of the logarithm inequality

    i just wonder why the symbol of inequality from <= changed to < only? how come?
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Super Member ILikeSerena's Avatar
    Joined
    Dec 2011
    Posts
    733
    Thanks
    121

    Re: solution set of the logarithm inequality

    Quote Originally Posted by rcs View Post
    i just wonder why the symbol of inequality from <= changed to < only? how come?
    In this particular case it did not change from <= to <.
    What you give as a solution is incorrect.
    The proper solution is the complement of the interval (-4,0).
    That is: x <= -4 or x >= 0.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 7
    Last Post: July 10th 2012, 10:22 AM
  2. Inequality with logarithm, help needed
    Posted in the Algebra Forum
    Replies: 4
    Last Post: August 15th 2010, 05:15 AM
  3. Solving inequality with logarithm
    Posted in the Algebra Forum
    Replies: 1
    Last Post: December 11th 2009, 02:59 PM
  4. Inequality with logarithm help needed.
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: July 24th 2009, 04:15 AM
  5. Solve Logarithm Inequality
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: April 14th 2009, 01:11 PM

Search Tags


/mathhelpforum @mathhelpforum