1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    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


    User Avatar
    Science Advisor

    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook