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What to do then?

  1. Oct 4, 2008 #1
    I tried to solve this exponential inequation , but i can't do more:

    5[tex]\sqrt[x]{64}[/tex] [tex]\geq[/tex] 625

    5*26/x>=625 dived by 5
    26/x>=125
    26/x>=53 and i have not idea what to do then
     
  2. jcsd
  3. Oct 4, 2008 #2

    symbolipoint

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    Raise both sides to the x/6 power and obtain 2 >= 5^(3x/6). Then simplify and obtain
    2 >= 5^(x/2)

    From there the steps no longer seem clear unless you know how to use rules of logarithms. Using base 2 or base 5 appear to offer no advantage, so take logarithms of both sides, base 10. (or base e if you prefer).
     
    Last edited: Oct 4, 2008
  4. Oct 4, 2008 #3
    but the answer sad that the result is:xE (0,3),so this don't need logarithms
     
  5. Oct 4, 2008 #4

    symbolipoint

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    Some of that solution is wrong. x cannot reasonably be too close to 3. Did you try using logarithms and resorting to a graphing calculator? x should be small, maybe very small. Anybody else? I might check more thoroughly, later.
     
  6. Oct 4, 2008 #5

    symbolipoint

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    I believe easiest to start from here,
    2^(6/x) >= 125
    and take logarithms by any base of both sides.
     
  7. Oct 4, 2008 #6
    There is no way I know of to get an exact answer for x without using logarithms. You can plug into a graphing calculator to get an approximate answer, but why not use logarithms?
     
  8. Oct 4, 2008 #7

    symbolipoint

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    I in fact solved the problem without using a graphing calculator; I also then posted the solution process but doing so was a violation of the rules of this forum so that post was deleted. Knowing about logarithms is truely necessary.
     
  9. Oct 5, 2008 #8

    HallsofIvy

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    27= 128 so you must have 6/x slightly less than 7. that means that x is slightly less than 7/6, or close to 1.
    I don't know what you meant by "but the answer said that the result is:xE (0,3),so this don't need logarithms " since many numbers in that interval can only be written as logarithms!
     
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