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    difference between log and log to the base 10

    HI
    can any one explain me difference between natural log and log of base ten.
    Thanks

    •   Alt7th June 2004, 10:36

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    natural log of pi

    A number can be represented by a first number raised to the exponent of a second number. The second number is call the logarithm and the first number is the base. The two most common bases are 10 and 2.7......

    The symbol for the first is Log and for the second Ln.



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    differnece between ln and log

    the reson of choosing 10 is obvious, but why e=2.7...?
    the answer is that it back to 300 years or more ago. to Euler (which e comes from his name). the function e^x is the only function that its derivative (and consequently its integral) is itself. {e^x'=e^x). no other function has this charasteristic. the number e could be achieved by several numerical and analytical methods, more often infinite summations.
    this number has more important rule in complex analysis.

    marti



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    difference between natural log and log of base ten

    And if you need to convert between them:
    log10(x) = ln(x) / ln(10)
    ln(x) = log10(x) / log10(e)



    •   Alt10th June 2004, 12:52

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    Re: difference between natural log and log of base ten

    y
    y = log (x) ==>find y: x = b
    b

    where b is the base (b = 10 or b = e)



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    Re: difference between natural log and log of base ten

    Thanks for your interesting reply. I did not realise the e comes from Euler's name until I real your post!

    By the way, does anybody know any history of the pi (3.14)?

    Quote Originally Posted by mamali
    the reson of choosing 10 is obvious, but why e=2.7...?
    the answer is that it back to 300 years or more ago. to Euler (which e comes from his name). the function e^x is the only function that its derivative (and consequently its integral) is itself. {e^x'=e^x). no other function has this charasteristic. the number e could be achieved by several numerical and analytical methods, more often infinite summations.
    this number has more important rule in complex analysis.

    marti



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    Re: difference between natural log and log of base ten

    Quote Originally Posted by no
    By the way, does anybody know any history of the pi (3.14)?
    Just use Google, it's very very easy to find!!!

    http://www.wordiq.com/definition/Pi

    http://www.campusprogram.com/referen...a/p/pi/pi.html

    http://www.briantaylor.com/Pi.htm

    There 100's of pages like this, no need to ask about it here.



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    Re: difference between natural log and log of base ten

    virology.wisc.edu/acp/Classes/ DropFolders/DropBioMod_lectures/M04-NatLogs.pdf


    there u go



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    Re: difference between natural log and log of base ten

    By the way, does anybody know any history of the pi (3.14)?
    Pi basically establishes the relationship b/w circumference and diameter.
    The ratio of circumference to diameter is pi.

    Note that pi=22/7 is just an approximation,thats why it not a rational but irrational number



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    difference between natural log and log of base ten

    You should read:

    e: The Story of a Number
    by Eli Moar

    for a more historical and detailed discussion.



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