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Properties of natural log and absolute value

  1. Sep 24, 2014 #1
    1. The problem statement, all variables and given/known data
    from -lnIxI to lnI x^-1I , I try to go from -lnIxI to lnI x^-1I by using some properties.


    2. Relevant equations
    - lnIxI


    3. The attempt at a solution
    First I write the -lnIxI as -1*lnIxI and then I use -1 as an exponent to absolute value of x in the natural log that is
    ln ( IxI^-1) and then I take -1 inside the paranthesis and I arrive to ln Ix^-1I which is also ln I 1/x I.

    Are my steps correct? If not, which step is incorrect?

    Thank you.
     
  2. jcsd
  3. Sep 24, 2014 #2

    Mark44

    Staff: Mentor

    Looks OK to me, but it's more wordy than it needs to be.
    ##-ln |x| = -1 * ln|x| = ln(|x|^{-1}) ##
    The last expression is the same as ##ln(\frac{1}{|x|})##
     
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