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Math Help - repeated division ... what formula to use ?

  1. #1
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    repeated division ... what formula to use ?

    im not sure what kind of formula to use for the below.

    i want to divide a variable number by a constant number and need to know how many times it took to divide it to get below x number?
    such as:
    4650 is the variable number, 6 is the constant, and 20 is x.
    4650 divided by 6, then the product of that divided by 6, etc etc.
    (4650/6=775--> 775/6-129.167--> 129.167/6=21.528--> 21.528/6=3.588)
    i need to know how many divisions it takes to get below x
    so somewhere between the 3rd and 4th division is the number im looking for.

    i need to be able to change the variable, but the constant and x would always be the same.

    does that make sense? any idea as to what kind of equation i need to use for this type problem?
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  2. #2
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    re: repeated division ... what formula to use ?

    have you been taught indices and logs? if so, solve this equation for n:

    V \cdot (\frac{1}{6^n}) = 20

    Spoiler:

    \frac{1}{6^n} = \frac{20}{V}

    \frac{1}{6^n} = \frac{20}{V}

    -n = \log_6 \frac{20}{V}

    -n = \frac{\ln \frac{20}{V}}{\ln 6}

    n = -1 \times \frac{\ln \frac{20}{V}}{\ln 6}

    (optional: simplify using log rules)
    n = \frac{\ln V - \ln 20}{\ln 6}

    in the case V=4650 this gives n=3.04, which is "somewhere between 3 and 4" as you expect. The number wont fall below x until the 4th division is completed.
    Last edited by SpringFan25; December 3rd 2011 at 10:58 AM. Reason: typo fixed
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  3. #3
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    re: repeated division ... what formula to use ?

    Quote Originally Posted by SpringFan25 View Post
    have you been taught indices and logs? if so, solve this equation for n:

    V \cdot (\frac{1}{6^n}) = 20
    i never was taught that or simply dont recall it. can you help educate me? do you know if this type equation can be solved in an excel spreadsheet formula?
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  4. #4
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    re: repeated division ... what formula to use ?

    The solution is given in the spoiler and is

    You will need to round the answer up if it isn't an integer.
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