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Exponential functions

  1. Apr 9, 2007 #1
    1. The problem statement, all variables and given/known data
    Solve the equation:
    (1/9)^m = 81^m + 4

    2. Relevant equations
    I know how to do a similar equation:
    9^2p = 27^p-1

    3^4p = 3^3p-1

    cancel out the 3's because the base is the same.

    4p = 3p-1
    -3p -3p

    1p = -1

    3. The attempt at a solution
    I know how to do ones like that but when it comes to this I start to struggle with fractions. :'(.

    I'm totally lost and cant even make an attempt to this equation. I'm not asking for the answer but just a maybe the first step or something to get me on the right path.
  2. jcsd
  3. Apr 9, 2007 #2
    How about converting some terms to powers of 9?
  4. Apr 9, 2007 #3
    [tex] (\frac{1}{9})^m = 81^{m+4} [/tex]

    [tex] (9^{-1})^m = (9^2)^{m+4} [/tex]

    [tex] (9)^{-m} = (9)^{2m+8} [/tex]

    [tex] -m = 2m+8 [/tex]

    [tex] -8 = 3m [/tex]

    [tex] m = - \frac{8}{3} [/tex]
  5. Apr 9, 2007 #4


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    The way you manage your notation is very important: you wrote
    which showed your original equation of difficulty to be very different from what you meant. In simple text-based expressiveness, you needed proper grouping saying (1/9)^m = 81^(m+4); The way you first wrote it, the "4" was not included as part of the exponent.
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