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Inequality Question

  1. Dec 4, 2011 #1
    is

    [itex]\frac{x-1}{x}[/itex]<ln(x)<x-1

    valid for 0<x<1

    I think it is I just want to get a second opinion.
     
  2. jcsd
  3. Dec 4, 2011 #2

    hunt_mat

    User Avatar
    Homework Helper

    One way to look at these things is to examine the functions:
    [tex]
    f(x)=\frac{x-1}{x}-\ln x\quad g(x)=\ln x-(x-1)
    [/tex]
    and compute the derivatives f'(x) and g'(x) and examine if f(x) and g(x) are increasing or decreasing functions and examine the values for certain points and the inequality should drop out.
     
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