Simple Algebra problem - Solving for 2 of the same unknown

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In summary, the equation ln(0.0693/0.0475) = (70435/8.314)((T3-298)/(T3*298)) can be simplified to 0.377 = 8471.9((T3-298)/(T3*298)), and then solved for T3 by multiplying both sides by the denominator of the right-hand side and expanding to obtain a simplified equation of (T3-298)/298 = 1/298 - 1/T3. From here, solving for T3 becomes easier.
  • #1
smaan
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Homework Statement



ln(0.0693/0.0475) = (70435/8.314)((T3-298)/(T3*298))

Solve for T3



Homework Equations





The Attempt at a Solution



The fact that there are 2 T3's is really throwing me off, I feel that I am doing something algebraically wrong.

0.377 = 8471.9((T3-298)/(T3*298))

How would I solve for T3?
 
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  • #2
smaan said:

Homework Statement



ln(0.0693/0.0475) = (70435/8.314)((T3-298)/(T3*298))

Solve for T3

Homework Equations



The Attempt at a Solution



The fact that there are 2 T3's is really throwing me off, I feel that I am doing something algebraically wrong.

0.377 = 8471.9((T3-298)/(T3*298))

How would I solve for T3?
[itex]\displaystyle \frac{T_3-298}{298T_3}=\frac{T_3}{298T_3}-\frac{298}{298T_3}[/itex]
[itex]\displaystyle =\frac{1}{298}-\frac{1}{T_3}[/itex]​
Now there's only one T3 .
 
  • #3
Sometimes I find "getting rid" of the fraction helpful for seeing the solution. Basically multiply both sides by the denominator (of the RHS) and expand. Then you collect like terms and everything else is easy.
 

1. How do I solve for two unknown variables in a simple algebra problem?

In order to solve for two unknown variables in a simple algebra problem, you need to have two equations with two variables. You can then use substitution or elimination to solve for one variable, and then plug that value into the other equation to solve for the second variable.

2. Can I solve for two of the same unknown variable in a single equation?

No, in order to solve for two of the same unknown variable, you need to have two separate equations with two different variables. This allows you to have enough information to solve for both variables.

3. How do I determine which variable to solve for first?

Typically, it is easier to solve for the variable that has a coefficient of 1 or -1. If both variables have coefficients other than 1 or -1, you can choose to solve for the variable that has the smallest coefficient, or the variable that is easier to isolate.

4. Can I use the same method to solve for two unknown variables in any algebra problem?

Yes, the same method of using two equations with two variables can be applied to solve for two unknown variables in any algebra problem, as long as the equations are independent and not redundant.

5. Are there any shortcuts or tricks to solve for two unknown variables in a simple algebra problem?

There are no specific shortcuts or tricks to solving for two unknown variables in a simple algebra problem. However, it is important to familiarize yourself with different algebraic techniques, such as substitution and elimination, to make the process more efficient.

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