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Homework Help: Simplify (Lnx)^2,3,4,5 etc.

  1. Mar 6, 2012 #1
    1. The problem statement, all variables and given/known data
    Im trying to simply (lnx)^n say (ln2)^3

    2. Relevant equations


    3. The attempt at a solution

    Im lost on this one I can't find any information. All info I'm finding is dilute because of similar search terms.

    Please, and thanks!
  2. jcsd
  3. Mar 6, 2012 #2
    There's no way to simplify it in the form you have? Are you sure it isn't meant to be read as ln(x^n) Where the exponent is in the natural log? If so, the rules of logarithms tell us that we can move the n to the front and write it as n*ln(x). So, how would this look for say ln(2^3)?
  4. Mar 6, 2012 #3
    no its (ln2)^4 not ln2^4=4ln2 solving this I believe involves setting it equal to σ or some variable and then exponentiating using e. Although I could be completely wrong. I know this can be simplified and solve because my professor did it in class, I just can't find my notes from that day.
  5. Mar 6, 2012 #4
    Well, letting (ln2)^4 and trying to solve for say 2 here, we'd have to involve a 4th root:

    Two solutions (for even roots):
    ln2 = 4-root(y) and ln2 = -4-root(y)

    So now, we can use e as:

    2=e^(4-root(y)) and 2=e^(-4-root(y))=1/e^(4-root(y))

    And of of course for odd roots it isn't necessary.

    Does this look similar?
  6. Mar 6, 2012 #5
    I think I'm following you've if 4-root(y) means y1/4. Regardless that doesn't look right? Thanks for the interest though :). We should be able to get a concrete answer like 16ln2 or something if i remember correctly!
  7. Mar 6, 2012 #6


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    Science Advisor
    Homework Helper

    No, ln(x)^n is just ln(x)^n. ln(x^n)=n*ln(x), but that's not what you are asking about.
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