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Simplifying ln

  1. Jun 26, 2006 #1
    hi quick question for this:
    simplify the following

    ln(4+4y+4y^2) i know i need to use those simplifying rules for ln which are ln(xy)=lnx+lny
    ln(1/x)=-lnx
    ln(x/y)=lnx-lny
    ln(x^r)=rlnx

    but for the question im asked to simplify.. it doesnt really follow any of these... I was wondering what the rule is for this type of question. Do i do:
    ln4+ln4y+ln4y^2?? Thanks!
     
  2. jcsd
  3. Jun 26, 2006 #2
    Notice 4 + 4y + 4y^2 = 4(1 + y + y^2), now use the fact that ln(ab) = lna + lnb.

    Careful here! It is not true in general that ln(a + b) = lna + lnb. Goodluck.
     
  4. Jun 26, 2006 #3
    ooops wrote the question wrong!

    woopsies wrote the question wrong... its actually ln(4+4y+y^2)
    so I arranged the inside so (y+2)(y+2) so can I use ln(ab) = lna + lnb
    so that ln(y+2)(y+2)=ln(y+2)+ln(y+2)??? Would that we right? Thanks
     
  5. Jun 26, 2006 #4

    arildno

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    Certainly!
    And, furthermore, this is consistent with:
    [tex]\log((y+2)^{2})=2\log(y+2)[/tex]
     
  6. Jun 28, 2006 #5

    VietDao29

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    There should be an absolute value there. :)
    It should read:
    [tex]\ln ((y + 2) ^ 2) = 2 \ln |y + 2|[/tex]
    Note that the domain of the LHS is all the reals but y = -2, so the domain of the RHS must also be all the reals but y = -2. And if you are working in the reals, ln(y + 2) is only defined for y > -2. :)
     
  7. Jun 28, 2006 #6

    arildno

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