How to re-arrange formula with an exponent

  • Context: High School 
  • Thread starter Thread starter wally6767
  • Start date Start date
  • Tags Tags
    Exponent Formula
Click For Summary

Discussion Overview

The discussion centers around the rearrangement of a formula involving an exponent, specifically solving for the variable Tp in the equation T = (Tp / Sa) to the 0.833 power. The context includes mathematical reasoning and problem-solving related to algebraic manipulation.

Discussion Character

  • Mathematical reasoning

Main Points Raised

  • One participant requests assistance in rearranging the formula to solve for Tp, expressing difficulty due to a long absence from school.
  • Another participant suggests taking logarithms of both sides to facilitate solving for Tp, providing a step-by-step approach involving logarithmic properties.
  • A different participant expresses frustration with the logarithmic method, stating they do not recall performing such calculations.
  • Another approach proposed involves taking the reciprocal of the exponent (1/0.833) and manipulating the equation directly without logarithms, leading to a solution for Tp.
  • A participant acknowledges the latter method as an elegant solution, indicating appreciation for the approach.

Areas of Agreement / Disagreement

There is no consensus on the method to solve for Tp, as participants present different approaches, with some favoring logarithmic manipulation and others preferring direct exponentiation.

Contextual Notes

Participants express varying levels of familiarity with the mathematical techniques involved, indicating potential limitations in their understanding of logarithmic properties and exponent rules.

wally6767
Messages
3
Reaction score
0
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
 
Mathematics news on Phys.org
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##.
 
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.
 
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].
 
hallsofivy, thank you very much for this elegant solution.
 

Similar threads

  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 17 ·
Replies
17
Views
3K
  • · Replies 12 ·
Replies
12
Views
3K
  • · Replies 3 ·
Replies
3
Views
5K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 12 ·
Replies
12
Views
3K
Replies
1
Views
3K
  • · Replies 49 ·
2
Replies
49
Views
7K
  • · Replies 2 ·
Replies
2
Views
2K
Replies
2
Views
3K