How Do You Correctly Solve This Complex Equation?

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SUMMARY

The discussion focuses on solving the equation Im = (Im + Ie + Ia)e^{-t/T} + Ia. The user encounters difficulties when manipulating the equation, particularly when transitioning from the second to the third line. Key insights include the importance of treating e^{-t/T} as a single entity rather than applying logarithmic functions unnecessarily. The correct approach involves rearranging the equation to isolate Im and simplifying by dividing both sides by e^{-t/T}.

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  • Familiarity with algebraic manipulation techniques
  • Basic knowledge of logarithmic functions
  • Concept of isolating variables in equations
NEXT STEPS
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Students in mathematics or engineering fields, educators teaching algebra and calculus, and anyone looking to improve their problem-solving skills in complex equations.

Matt007
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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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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.
 
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
 

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