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Find all values of x which satisfy the inequality

  • Thread starter Petkovsky
  • Start date
  • #1
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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
 

Answers and Replies

  • #2
nicksauce
Science Advisor
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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?
 
  • #3
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Find all values of x which satisfy the inequality. Sorry i didnt mention, i thought it was clear.
 
  • #4
tiny-tim
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6^(2x+3) < 2^(x+7) * 3^(3x-1)
Hi Petkovsky! :smile:

Hint: take logs. :wink:
 
  • #5
Gib Z
Homework Helper
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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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