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What is 5^n=80n

  1. May 4, 2005 #1
    I've got a problem with this:
    find n!
    I can't solve out this one.
    thanx for ur help, I'm not sure if it's the right place for this thread.
  2. jcsd
  3. May 4, 2005 #2
    If [tex]n \in \mathbb{Z}[/tex], there is no such number.
  4. May 4, 2005 #3


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    5^x - 80*x = 0
    plot it
    and so far ive found 2 solutions (oh and there are no solns in Z of course)

    Approximate roots are:

    Last edited: Oct 8, 2005
  5. May 4, 2005 #4


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    Anyway the 2 exact solutions (in real numbers) are:

    [tex]n = -\frac{\text{ProductLog} \left( - \frac{\ln 5}{80} \right)}{\ln 5}[/tex]


    [tex]n = -\frac{\text{ProductLog} \left(-1, - \frac{\ln 5}{80} \right)}{\ln 5}[/tex]

    Which works out to 100 sf.:

    n = 0.01275934595849510712320293028417381446823346765193827957982622843955432250672941443435143426214944153


    n = 3.501327193786496727104387840526356291207393167955463046140101380079871277483867981890189846055191784
  6. May 5, 2005 #5


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    and that is an 'analytical' solution?
  7. May 8, 2005 #6
    thanx for ur replies
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