1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    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!
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook