How to re-arrange formula with an exponent

  • Thread starter wally6767
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  • #1
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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
 

Answers and Replies

  • #2
jbunniii
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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##.
 
  • #3
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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.
 
  • #4
HallsofIvy
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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].
 
  • #5
3
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hallsofivy, thank you very much for this elegant solution.
 

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