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Logarithm inequality

  1. Feb 5, 2013 #1
    1. The problem statement, all variables and given/known data
    3 - 3^(x+1) < 5^x - 15^x

    3(1-3^x) < 5^x(1-3^x)

    Do I have to impose 1-3^x > 0 ?

    It results x<0 and x>log(5,3) but book has written 0 < x < log(5,3) where did I wrong ?
  2. jcsd
  3. Feb 5, 2013 #2


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    hi scientifico! :smile:

    (try using the X2 button just above the Reply box :wink:)
    no, you can't do that, you don't know that it's true!

    either you must deal separately with 1-3x > 0 and 1-3x < 0.

    or just write (1-3x)(3-5x) < 0 :wink:
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