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Logarithm overkill!

  1. Jan 23, 2008 #1
    Hello again!
    I have been working on this log, and the longer I work on it, the more confused I get! Here's the problem:
    Find the exact value for:

    [tex]ln(ln[e^{e^{5}}[/tex]])

    ----
    Here's what I've tried so far:

    [tex]e(ln[e^{e^5}}[/tex]])

    [tex]e^{x} = ln(e^{e^5}}) [/tex]
    [tex]e^{x} = e^{e^5}}[/tex]
    [tex]e^{5} = (2.72)^{5}[/tex]
    [tex]e^{x} = e^{149}[/tex]
    [tex]x = 149 [/tex]

    ....I have no idea if I'm doing this right, but I'm not feeling like I am...Help?
     
  2. jcsd
  3. Jan 23, 2008 #2
    use the property that Ln(a^b) = b Ln(a), Ln(e) = 1, Ln(e^a) = a
     
  4. Jan 23, 2008 #3

    rock.freak667

    User Avatar
    Homework Helper

    z=ln(lne^(e^5)). Use the definition of a log now.
     
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