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Log Problem

  1. Apr 24, 2006 #1
    Here is a problem that I was presented in my math class using logs and my entire group is stumped:

    Peter deposits $800 into an investment fund that earns 8% per year, compounded annually. Mary Jane deposits $1000 into an investment fund that earns 6% per year, compounded annually? When will their investments be equal?

    This is what we have so far:

    800(1.08)^x = 1000(1.06)^x
    0.8(1.08)^x = 1.06^x

    log1.08(800) = x
    log1.06(1000) = x

    log1.08(800) = log1.06(1000)
    log800/log1.08 = log1000/log1.06 (This does not work; they are not equal)

    What did I do wrong and could someone please help me get the answer? Thanks
     
  2. jcsd
  3. Apr 24, 2006 #2

    dav2008

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    Gold Member

    How exactly did you get from your second to third/fourth lines?
     
  4. Apr 24, 2006 #3

    NateTG

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    Science Advisor
    Homework Helper

    You made some sort of strange jump from:
    [tex]0.8 \times 1.08^x= 1.06^x[/tex]
    to
    [tex]log_{1.08}800=x[/tex]

    Perhaps you could try something else from
    [tex]0.8 \times 1.08^x= 1.06^x[/tex]
    like dividing both sides by [itex]1.08^x[/itex]
     
  5. Apr 24, 2006 #4
    Thanks for the help, but I just saw my major mistake. Here are my corrections:

    (800)(1.08)^x = (1000)(1.06)^x
    (1.08)^x = 1.25(1.06)^x
    (1.08/1.06)^x = 1.25
    (1.0189)^x = 1.25
    xlog(1.0189)^x = log1.25 [Note: The bases are 10]
    x = log1.25/log1.0189
    x = 11.9
    ----> 12

    Thanks again for your help.
     
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