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Find all values of x which satisfy the inequality

  1. Jun 2, 2008 #1
    6^(2x+3) < 2^(x+7) * 3^(3x-1)

    So what i did first was:

    3^(2x+3) * 2^(2x+3) < 2^(x+7) * 3^(3x-1)

    Now i dont know how to set up the equation. I guess this is not correct

    2*(2x+3) < x+7 + 3x - 1
     
  2. jcsd
  3. Jun 2, 2008 #2

    nicksauce

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    First of all, what is it that you're trying to do? Find for which x this is true? Show that it is always true? Show that it is never true?
     
  4. Jun 2, 2008 #3
    Find all values of x which satisfy the inequality. Sorry i didnt mention, i thought it was clear.
     
  5. Jun 2, 2008 #4

    tiny-tim

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    Hi Petkovsky! :smile:

    Hint: take logs. :wink:
     
  6. Jun 3, 2008 #5

    Gib Z

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    We needn't even take logs, the numbers happen to work out very nicely =]

    Q: Find x such that; [tex]6^{2x+3} < 2^{x+7} \cdot 3^{3x-1}[/tex].

    Rewrite the exponents on the RHS to also have 2x+3's, [tex] RHS = \frac{2^{2x+3}}{2^{x-4}} \cdot 3^{2x+3} 3^{x-4} = 6^{2x+3} \left( \frac{3}{2} \right)^{ x-4} [/tex].

    The question is much easier in this form.
     
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