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Please help with this exp. equation

  1. Oct 3, 2009 #1
    2^x=x^10

    ln(2^x)=ln(x^10)
    x*ln(2)=10*ln(x)
    ln(2)/10=ln(x)/x

    from here how can i solve this??

    i seem to keep on going in circles
     
    Last edited: Oct 3, 2009
  2. jcsd
  3. Oct 3, 2009 #2
    You won't be able to find an explicit or exact answer for this kind of problem.
     
  4. Oct 3, 2009 #3
    how can i go about it then?
     
  5. Oct 3, 2009 #4

    LCKurtz

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    Numerically. Maple gives 1.077550150.
     
  6. Oct 3, 2009 #5
    ...n
     
    Last edited: Oct 3, 2009
  7. Oct 3, 2009 #6
    i looked the Lambert W function up, and using it i get,

    2x=x10
    (21/10)x=x
    1=x/(21/10)x =====> (21/10)=a
    1=x/ax
    1=x*e-x*ln(a)
    -ln(a)=[(-ln(a)*x)*e(-ln(a)*x)

    after applying W to each side

    -ln(a)*x=W(-ln(a))
    x=W(-ln(a)/-ln(a))

    is this correct, and also how do i get a numerical answer for this??
     
  8. Oct 3, 2009 #7

    LCKurtz

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    You might as well have solved the original equation numerically.
     
  9. Oct 3, 2009 #8
    how would i have done that
     
  10. Oct 3, 2009 #9

    LCKurtz

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    Newton's method for one.
     
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