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How to re-arrange formula with an exponent

  1. Jul 4, 2013 #1
    I have been out of school for 35 years and this is out of my reach. Can someone please re-arrange this formula solved for Tp .

    T = (Tp / Sa) to the .833 power

    I have an example in it's current form.

    T = 40.5 Deg C
    Tp = 2300mW/CM cubbed
    Sa = 27 CM squared
  2. jcsd
  3. Jul 4, 2013 #2


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    First take logs of both sides:
    $$\log(T) = \log\left( (Tp/Sa)^{0.833}\right) = 0.833 \log\left( (Tp/Sa) \right) = 0.833(\log(Tp) - \log(Sa))$$
    Now solve for ##\log(Tp)## and exponentiate both sides to get an expression for ##Tp##.
  4. Jul 4, 2013 #3
    jbunnii, thanks for the reply. I have tried to solve for Tp but no luck. I do not remember ever doing math like this before.
  5. Jul 5, 2013 #4


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    Since the "target" variable is not in the exponent, I would not use the logarithm, I would take the 1/.833 power of both sides:
    [tex]T= \left(\frac{T_p}{S_a}\right)^{.833}[/tex]
    [tex]T^{1/.833}= \frac{T_p}{S_a}[/tex]
    [tex]T_p= T^{1/.833}S_a[/tex].
  6. Jul 5, 2013 #5
    hallsofivy, thank you very much for this elegant solution.
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