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Homework Help: Inequality Problem from Spivak's Calculus: Chapter 1, Problem 4, Subproblem XI

  1. Jul 10, 2010 #1
    1. The problem statement, all variables and given/known data
    Find all numbers x for which:

    2x<8


    2. Relevant equations



    3. The attempt at a solution

    I really haven't been able to figure this one out.
     
  2. jcsd
  3. Jul 10, 2010 #2
    Do you have any calculations to show?

    I assume it means integer values? If so surely isn't it just:

    [tex]x=-\infty, ..., 0, \pm 1, \pm 2, \pm 3[/tex]

    Unless I'm missing the point somewhere? It seems a bit simple though.

    :smile:
     
  4. Jul 10, 2010 #3

    hunt_mat

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    Homework Helper

    Note that [tex]8=2^{3}[/tex], 2^{x} in monotonically increasing. So the question is, what values of x satisfy
    [tex]
    2^{x}<2^{3}
    [/tex]
    can you say what values satisfy this equation?
     
  5. Jul 10, 2010 #4
    Stated in a different way, [itex]\log_2(t)[/itex] is an increasing function. Inequalities remain true if you apply an increasing function.
     
  6. Jul 10, 2010 #5
    Sorry I wasn't very clear.

    Just thinking it through I know that 23 is 8, so x<3.

    However my difficulty was in proving it, using the mathematical context that Spivak uses.

    hunt_mat's example makes a lot of sense to me and fulfills that need to explain it more concretely.

    Thanks for your help!
     
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