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Math Help - Help with an inequality.

  1. #1
    Junior Member
    Joined
    Sep 2008
    Posts
    40

    Help with an inequality.

    3\ln2<2\ln(x)<2\ln3

    Express the solution x as a set using the notations ()[]

    Can anyone help me out?

    EDIT: Please don't skip any steps that may seem arbitrary to you =] thanks again
    Last edited by jpatrie; October 2nd 2008 at 09:09 PM.
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  2. #2
    MHF Contributor
    Joined
    Apr 2008
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    1,092
    We begin:

    3 \ln 2 < 2 \ln 2x < 2 \ln 3

    (3/2) \ln 2 < \ln 2x < \ln 3

    \ln (2^{3/2}) < \ln 2x < \ln 3

    Since the natural logarithm is an increasing function, we have:

    2^{3/2} < 2x < 3

    2\sqrt{2} < 2x < 3

    \sqrt{2} < x < 3/2
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