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Problem with a logarithmic rule

  1. Jan 30, 2013 #1
    lnrules_zps48d61963.jpg

    Please could some one help me with the rules of logarithms to understand why inverting the numbers in the bracket and change the minus sign to a plus sign gives the same result?

    Thank you
     
  2. jcsd
  3. Jan 30, 2013 #2

    mfb

    User Avatar
    2017 Award

    Staff: Mentor

    ln(a^b)=b*ln(a)
    Try b=-1
     
  4. Jan 30, 2013 #3

    Mark44

    Staff: Mentor

    ln(A/B) = ln(A) - ln(B) = -[ln(B) - ln(A)] = -ln(B/A)
     
  5. Jan 30, 2013 #4
    for the equation on the right: t= ( ln (N0/N) ) / λ:

    if you multiply top and bottom of the fraction by -1 you get

    t= (-1 ln (N0/N)) / -λ

    You have -1 ln (N0/N) which is equal to ln( (N0/N)^-1 ) by the power rule. The (N0/N)^-1 inside the log flips to (N/N0) from the negative exponent and you get:

    t= ( ln (N/N0) ) / -λ.
     
  6. Jan 31, 2013 #5
    Fantastic thanks to you all
     
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