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What is LN?

  1. Sep 22, 2005 #1
    What is LN? (Example problem requested)

    What is LN in math, and how do you solve the LN of something?
     
    Last edited: Sep 22, 2005
  2. jcsd
  3. Sep 22, 2005 #2

    TD

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    The "ln", nowadays also just denoted as "log" is the natural (or neperian) logarithm, meaning the one with base e (2.718...)
     
  4. Sep 22, 2005 #3
    ln is called the natural logarithm in math. It is a logarithm with a base of [itex]e[/itex]

    [tex]\ln{x}=\log_{e}x[/tex]

    We use ln as shorthand notation but the above notation is equally correct.

    To take to natural log of some number, let's call it A, is to find another number, let's call it B, so the [tex]e^B=A[/tex]

    Hope that gets you started.
     
  5. Sep 22, 2005 #4
    Erhm... My friend doesn't know what a logarithm is.

    Refresh his memory, please? x.x


    EDIT: Durr, posted while I typed. Thanks! Y.Y

    Lemme make sure I have this clarified.

    Let's make A = 27 and B = 3.
    (can't use latex here)

    Loga = B
    Log(27) = 3
    E^3=27
    E = 3

    Is this right, or am I confused?

    Give me an example problem, step by step, please. >_<
     
    Last edited: Sep 22, 2005
  6. Sep 22, 2005 #5
    Logarithm is the inverse of power. Logorithm goe as such:

    10^logx_base 10=x

    Exempe:

    10^x_base10=100
    10^x_base10=10^2

    x_base10=2.

    ln is base with base e. If you are wondering what is e, if you integrate the area of the function y=1/x between x=1 and x=a, the only solution for a that gives an area of 1 unit is e.

    We write log_baseex simply as lnx.

    An exemple is;

    5^x=4

    You can solve this with logs;

    (10^log5)^x=10^log4

    10^(xlog5)=10^log4

    xlog5=log4
    x=log4/log5

    The basic relationships

    a=log(xy)
    a=log((10^logx)(10^logy)
    a=log(10^logx + logy)

    Since we know that

    10^log(xy)=10^logx + logy,

    then

    log(xy)=logx + logy
     
    Last edited: Sep 22, 2005
  7. Sep 22, 2005 #6
    Sorry, this is incorrect. [itex]e[/itex] is a constant. It is defined as [tex]\lim_{x\rightarrow\infty}\left(1+\frac{1}{x}\right)^{x}[/tex] and is around 2.71.

    You won't be able to calculate numbers such as [itex]\ln 5[/itex] or [itex]\ln 1000[/itex] by hand. I'll use your numbers as an example.

    [tex]\ln x = \log_{e}x[/tex]

    So let's say that [tex]\log_{e}A=B[/tex]

    that means that [tex]e^B=A[/tex]

    You said A was 27 in your previous post. If you typed in [itex]\ln 27[/tex] in your calculator, it would tell you the exponent that if you took [itex]e[/itex] to that exponenet, it would equal 27.
     
  8. Sep 22, 2005 #7
    ln(a) is the area under the graph y=1/x limited by the lines x=1 and x=a.
     
  9. Sep 22, 2005 #8
    TD,

    Isn't that spelled "Naperian" logarithm?
     
  10. Sep 23, 2005 #9

    TD

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    That's quite possible, I tried translating it from my language :smile:
    Both get google hits but yours a bit more, so it's probably "Naperian" :tongue2:
     
  11. Sep 23, 2005 #10

    HallsofIvy

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    "Naperian" (notice that both Loren Booda and I are capitalizing it) is named for John Napier (apparently the "i" got lost somewhere), a Scottish mathematician- you don't "translate" people's names! Napier also, by the way, invented the decimal point.
     
  12. Sep 23, 2005 #11

    TD

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    In Dutch, it's called the 'Neperiaanse' or 'Neperse' logarithm, and I tried to "translate" that into English. I'm aware of the fact that it comes from a person, but that doesn't change the fact that the term is different in multiple languages.
    Of course, his name is the same everywhere, but the term for the logarithm (which was derived from his name) can be different in other languages.
     
    Last edited: Sep 23, 2005
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