How Do You Correctly Solve This Complex Equation?

In summary, the conversation is about someone trying to solve an equation involving Im, Ie, Ia, t, and T. The person is having trouble getting the equation to work and is asking for help. The expert advises to divide both sides by e^-t/T and suggests an alternative approach of expanding line 1 and rearranging the terms to make Im the focus.
  • #1
Matt007
7
0

Homework Statement



Hi,
I am trying to solve the equation for I am and am having trouble

[tex]Im=(Im+Ie+Ia)e^{-t/T} +Ia)[/tex]

[tex]Im-Ia = (Im+Ie+Ia)e^{-t/T})[/tex]


[tex]ln^{Im-Ia}= Im+Ie+Ia[/tex]




this is were I get to but can't get the equation to work. Have I don't something incorrect in the second line when moving e^-t/T across to the other side?

Thanks
 
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  • #2
Going from the second to the third line, there's something wrong.

Keep in mind [tex]\frac{1}{e^{-x}}[/tex] = [tex]e^{x}[/tex]. But expanding line 1 and rearranging the terms to make I am the focus may be the better alternative.
 
  • #3
Matt007 said:

Homework Statement



Hi,
I am trying to solve the equation for I am and am having trouble

[tex]Im=(Im+Ie+Ia)e^{-t/T} +Ia)[/tex]

[tex]Im-Ia = (Im+Ie+Ia)e^{-t/T})[/tex]


[tex]ln^{Im-Ia}= Im+Ie+Ia[/tex]
Since you are not solving for t or T there is no reason to take a logarithm. Just treat [itex]e^{-t/T}[/itex] as a single number and divide both sides by it:
[tex]Ime^{t/T}- Iae^{t/T}= Im+ Ie+ Ia[/tex]

Can you solve from there?




this is were I get to but can't get the equation to work. Have I don't something incorrect in the second line when moving e^-t/T across to the other side?

Thanks
 

FAQ: How Do You Correctly Solve This Complex Equation?

1. What is a complex equation?

A complex equation is an equation that contains at least one variable that has both a real and imaginary part. It can also involve operations such as addition, subtraction, multiplication, division, and exponentiation.

2. How do I solve a complex equation?

The first step in solving a complex equation is to simplify it as much as possible. Then, you can use various techniques such as substitution, factoring, or the quadratic formula to solve for the variable.

3. Can I use a calculator to solve a complex equation?

Yes, you can use a calculator to solve a complex equation. However, it is important to understand the steps involved in solving the equation manually in case the calculator gives an incorrect result or is not available.

4. What are the common mistakes to avoid when solving complex equations?

Some common mistakes to avoid when solving complex equations include missing or incorrect signs, incorrect order of operations, and forgetting to distribute terms. It is important to double-check your work and be meticulous in your calculations.

5. Are there any tips for solving complex equations more efficiently?

One tip for solving complex equations more efficiently is to break them down into smaller, simpler equations. You can also try to identify patterns or common factors in the equation. It is also helpful to practice regularly and familiarize yourself with different techniques for solving equations.

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