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Moving exponent

  1. Jan 4, 2010 #1
    Hello,

    I am having trouble getting my head around this:

    Can someone explain why
    [tex]x^{x}[/tex] = [tex]e^{xlgx}[/tex]

    I cannot seem to understand why this is true. I am quite weak when it comes to handling exponentials. I dare say that I am terrified of e!

    Also, would this also hold for a static power: so [tex]x^{a}[/tex]

    Thanks,

    Luca
     
  2. jcsd
  3. Jan 4, 2010 #2
    Remember that for a > 0, [tex]\ln ( a^b ) = b \ln a[/tex] and the fact that exponentation and the natural logarithm are inverse functions.
     
  4. Jan 4, 2010 #3
    That makes sense!

    Many thanks!
     
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