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Natural logarithms

  1. Apr 26, 2004 #1

    phy

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    i need help with this one question; we have to write ln9-3ln(squareroot 3) + ln81 in the form kln3 where k is an exact fraction; i dont remember how to do this at all so any help would be greatly appreciated; thanks
     
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  3. Apr 26, 2004 #2

    arildno

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    Remember the general rule : ln(a^(b))=b*ln(a)
     
  4. Apr 26, 2004 #3

    phy

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    so i could rewrite it as 2ln3-3ln(sqrt3)+4ln3; but then what?
     
  5. Apr 26, 2004 #4
    Remember that taking the square root is the same as raising to the 1/2 power. You may also want to combine the logs before making the exponents into the coefficients. Do you remember your log properties?
     
  6. Apr 26, 2004 #5

    phy

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    um, not really
     
  7. Apr 26, 2004 #6

    arildno

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    Use Moose352 suggestion of sqrt(3)=3^(1/2). You will now have ln(3) as a common factor.
     
  8. Apr 26, 2004 #7

    phy

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    so would the answer just be 4(4/3)ln3?
     
  9. Apr 26, 2004 #8

    arildno

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    How did you get the 1/3 denominator????
     
  10. Apr 26, 2004 #9

    phy

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    well i said that 3ln(sqrt3) is the same as 3ln(3^1/2) which is the same as 3/2(ln3)
     
  11. Apr 26, 2004 #10

    arildno

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    I'm with you there, that's correct.
    But it's 2 in the denominator not 3!
     
  12. Apr 26, 2004 #11

    phy

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    yeah so dont we do 3*1/2 which is 3/2? i'll show you what i've done so far.
    2ln3-3/2ln3+4ln3
    (4ln3)(2ln3)/(3/2ln3)
    4(4/3)ln3
     
  13. Apr 26, 2004 #12

    arildno

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    Allright, I see were you have mixed up:

    Sum rule logarithm: ln(x)+ln(y)=ln(x*y)
    This is not what you have done.
    Exponent rule logarithms: ln(a^(b))=b*ln(a)

    If you want to do it with the sum rule, write:

    2ln(3)-3/2ln(3)+4ln(3)=ln(3^(2))+ln(1/(3^(3/2)))+ln(3^(4))=
    ln(3^(2-3/2+4))=ln(3^(9/2))=9/2ln(3)

    I'll check up on this thread tomorrow..
     
  14. Apr 26, 2004 #13

    phy

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    ok i get it now; i see where i made my mistake. thanks a lot for your help :)
     
  15. Apr 27, 2004 #14

    arildno

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    A good advice:
    When doing maths you are not too familiar with, keep the definitions right in front of you while you're working, until you don't need to look at them anymore.
     
  16. Apr 27, 2004 #15

    phy

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    yeah, that is good advice; it's just that that was a review question from my calculus textbook, stuff that we learned in highschool and haven't seen in some time; we were just expected to remember how to do it and i forgot; well, thanks for all your help
     
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