1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

What is 5^n=80n

  1. May 4, 2005 #1
    I've got a problem with this:
    5^n=80n
    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

    cronxeh

    User Avatar
    Gold Member

    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:

    n=0.012759
    n=3.50133
     
    Last edited: Oct 8, 2005
  5. May 4, 2005 #4

    Zurtex

    User Avatar
    Science Advisor
    Homework Helper

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

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

    and

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

    Which works out to 100 sf.:

    n = 0.01275934595849510712320293028417381446823346765193827957982622843955432250672941443435143426214944153

    And:

    n = 3.501327193786496727104387840526356291207393167955463046140101380079871277483867981890189846055191784
     
  6. May 5, 2005 #5

    cronxeh

    User Avatar
    Gold Member

    and that is an 'analytical' solution?
     
  7. May 8, 2005 #6
    thanx for ur replies
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: What is 5^n=80n
  1. What the value of n ? (Replies: 1)

Loading...