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Solve for the variable?

  1. Feb 16, 2010 #1
    1. The problem statement, all variables and given/known data

    Solve for N:

    AN^(β) = AN^(β - 1)T^(1-β)

    2. Relevant equations

    3. The attempt at a solution

    Here's what I got:

    AN^(β) = AN^(β - 1)T^(1-β)

    AN^(β) = AN^(β)N^(-1)T^(1)T^(-β)

    AN^(β) = AN^(β)T / NT^(-β)

    NAN^(β) =AN^(β)T / T^(-β)

    N = T/T^(-β)
  2. jcsd
  3. Feb 17, 2010 #2


    Staff: Mentor

    First off, divide both sides by A.
    Then divide by the appropriate quantity so that you have N to some power all by itself on one side.

    It's a pretty simple problem if you do the steps above.
  4. Feb 17, 2010 #3

    AN^(β) = AN^(β-1)T^(1-β)

    N^(β) = N^(β)N^(-1)TT^(-β)

    1 = N^(-1)TT^(-β)

    N = TT^(-β)

    Still getting the same thing.
  5. Feb 17, 2010 #4


    Staff: Mentor

    It's correct but can be written more simply as N = T1 - β

    In your first post, you have a lot of extra steps that you don't need.
    ANβ = ANβ-1Tβ-1
    <==> Nβ = Nβ-1Tβ-1 (divide both sides by A)
    <==> Nβ / Nβ-1 = Tβ-1 (divide both sides by Nβ-1
    <==> N = Tβ-1
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