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Another Logarithm problem

  1. Jan 18, 2009 #1
    1. The problem statement, all variables and given/known data
    This one has has me pretty lost, I'm not at all sure what to do, I've tried a couple of things. I have to find x.

    2(x-1) = 5(73x)

    2. Relevant equations
    Logarithm laws?

    3. The attempt at a solution
    (did multiple attempts but my most reasonable to my account)

    2(x-1) = 5(73x)
    [2(x-1)/5] = 73x
    [(x-1) log 2/5] = 3x log 7
    (x-1) log 2 = 5(3x*log 7)
    (x-1) log 2 = 15x * 5 log 7
    (x-1) log 2 = 15x * log 75
    (x-1) log 2 = 15x * log 16807
    x-1 = (15x * log 16807) / (log 2)
    x-1 = 15x * 14.034
    x = 15x * 14.034 + 1
    x = 15x * 15.034
    x/15x = 15.034
    1/15x = 15.034
    x = 15.034 * (1/15)
    x = 210.51

    I believe I am completetly off and I really can't figure this out, help will be appreciated!
     
  2. jcsd
  3. Jan 18, 2009 #2
    Hi,
    Try taking the log right away:

    (x-1)ln2 = ln5 + 3xln7
    xln2 - 3xln7 = ln5 + ln2
    x = (ln5 + ln2) / (ln2 - 3ln7)

    Not a very satisfying answer, is it?

    Regards, BobM
     
  4. Jan 18, 2009 #3
    Thank you, that is very helpful, I understand how you got from
    xln2 - 3xln7 = ln5 + ln2
    to
    x = (ln5 + ln2) / (ln2 - 3ln7)

    but I don't really understand what happened with the (x-1) when you go from
    (x-1)ln2 = ln5 + 3xln7
    to
    xln2 - 3xln7 = ln5 + ln2

    Thank you in advanced.
     
  5. Jan 18, 2009 #4
    I understood what was done!

    (x-1)ln2 = ln5 + 3xln7
    x ln 2 - ln 2 = ln 5 + 3xln7
    x ln 2 - 3x ln 7 = ln 5 + ln 2
    x (ln 2 - 3 ln 7) = ln 5 + ln 2
    x = ln 5 + ln 2 / ln 2 - 3 ln 7

    Thanksss!
     
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