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Math Help - finding simpler expressions for the quantities

  1. #1
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    Post finding simpler expressions for the quantities

    i'm just not seeing it for these:
    ln(e^(e^(x))
    and
    ln(e^(2lnx)

    i don't know where to begin!
    and is this one correct
    ln(e^secx)= ln(e)^secx= secxlne=secx
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  2. #2
    Super Member 11rdc11's Avatar
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    Quote Originally Posted by genlovesmusic09 View Post
    i'm just not seeing it for these:
    ln(e^(e^(x)) = e^x
    and
    ln(e^(2lnx) = ln x^2

    i don't know where to begin!
    and is this one correct
    ln(e^secx)= secx
    ln and e are inverses so they reduce y=x. Does this make sense? Ienteredthe right answers in for you
    Last edited by 11rdc11; September 8th 2009 at 09:47 PM.
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  3. #3
    MHF Contributor
    Grandad's Avatar
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    Hello genlovesmusic09
    Quote Originally Posted by genlovesmusic09 View Post
    i'm just not seeing it for these:
    ln(e^(e^(x))
    and
    ln(e^(2lnx)

    i don't know where to begin!
    and is this one correct
    ln(e^secx)= ln(e)^secx= secxlne=secx
    Two of the basic properties of logarithms (to any base, a) are:

    • \log_a(p^q)=q\log_a(p)


    • \log_a(a)=1, and in particular, \ln(e)=1

    So, if we apply these to your two questions:

    \ln(e^{(e^x)})=e^x\ln(e)=e^x

    and \ln(e^{2\ln (x)})=2\ln (x)\ln(e)=2\ln(x), which you can write as \ln(x^2) if you like (again using the first of these laws).

    Grandad
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