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Do Logarithms play any major part in being able to do calculus?

  1. Feb 18, 2008 #1
    do Logarithms play any major part in being able to do calculus?
     
  2. jcsd
  3. Feb 18, 2008 #2

    mgb_phys

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    More the other way around - the definition of ln() and 'e' are based on calculus.
     
  4. Feb 18, 2008 #3
    but how are they based on calculus?
     
  5. Feb 18, 2008 #4

    mgb_phys

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    The definition of ln(a) is the integral of 1/x from 0 to 'a'
     
  6. Feb 18, 2008 #5
    From 1 to a, not 0.
     
  7. Feb 18, 2008 #6

    mgb_phys

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    do'h sorry
     
  8. Feb 18, 2008 #7

    lurflurf

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    Your definition not everyones. It would be fair to say that many standard definitions use some concept of limit (i.e. use calculus) and many that do not use inequalities that are very limit like. Also we would like log to be continous, a calculus (or topology) concept.
     
  9. Feb 19, 2008 #8
    ok so one of my teachers told me that the number e came from (1+1/n)^n as n Approaches infinity but now do you get 2.71828182846........ from (1+1/n)^n
     
  10. Feb 19, 2008 #9

    mgb_phys

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    Try it! Just put in the first few terms.
    To answer your original question, 'e' comes up in a few standard calculus solutuions.
    And obviously knowing the rules about multiplying and adding exponents comes into a lot of calculus.
     
  11. Feb 19, 2008 #10
    is e a ratio?
     
  12. Feb 19, 2008 #11

    mgb_phys

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    No, it's an irrational number, that means that it can't be written as a/b.
    Actually it's also a trancendental number - meaning it can't be written as any equation with a finite number of terms, just like pi.
     
    Last edited: Feb 19, 2008
  13. Feb 20, 2008 #12
    ok so the number e [tex]\approx[/tex] (1+1/n)^n
     
  14. Feb 20, 2008 #13

    mgb_phys

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    I suppose a mathematician would say that e was exactly (1+/1n)^n for infiinite 'n'
     
  15. Feb 20, 2008 #14

    HallsofIvy

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    Not until you tell us what n is! Yes, for very large n, e is approximately that.

    Not unless he/she were speaking very loosely. 'n' is never infinite. What is strictly true is that [itex]e= \lim_{n\rightarrow \infty}(1+ 1/n)^n[/itex].
     
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