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Homework Help: Really Really Quick Questions!

  1. Feb 21, 2007 #1
    I just got my calculus midterm back, and I lost one mark on an area problem. I did the problem properly, but I may have made a mistake at the end.

    I end up with arctan1-1/2ln3-1/2ln1 (this step did not have an "x")
    I simplified this to pi/4-1/2ln3 (here, the grader put a 2 over my 3 in ln3)
    then I made it pi/4-ln(3^1/2) (there was a question mark around this)

    so my quick questions are:

    why was there are 2 over my three? (I thought 1/2ln1 was equal to zero.)
    why was there a question mark around the last part (I thought alnx was equal to ln(x^a)

    Hopefully this makes sense, post and I can clarify :biggrin:

    thanks SO much in advance if you helped!
  2. jcsd
  3. Feb 21, 2007 #2


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    It appears to me that the marker is unsure on properties of logarithms--you are correct.

    The correct properties are: loga-logb=log(a/b) (1) and alogb=log(ba).

    I can only think the marker has thought that ln3-ln1=ln(3-1)=2.* This is not correct. Of course, ln1=0. You can simplify the expression using (1) to give ln3-ln1=ln(3/1)=ln3.
    Again, this is correct.
    edit:*In retrospect, I don't see where the marker got ln2 from, since the expression would be -1/2{ln3+ln1} which, would become -1/2{ln4} using the incorrect rule. Anyway, the fact remains that you are correct.
    Last edited: Feb 21, 2007
  4. Feb 21, 2007 #3
    Ok thanks! That's what I thought...hopefully I'll be able to get my prof to change my mark!
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