How Do You Correctly Solve This Complex Equation?

[Matt007]

Homework Statement

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

$$Im=(Im+Ie+Ia)e^{-t/T} +Ia)$$

$$Im-Ia = (Im+Ie+Ia)e^{-t/T})$$


$$ln^{Im-Ia}= Im+Ie+Ia$$




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

 

[Zryn]

Going from the second to the third line, there's something wrong.

Keep in mind $$\frac{1}{e^{-x}}$$ = $$e^{x}$$. But expanding line 1 and rearranging the terms to make I am the focus may be the better alternative.

 

[HallsofIvy]

Homework Statement

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

$$Im=(Im+Ie+Ia)e^{-t/T} +Ia)$$

$$Im-Ia = (Im+Ie+Ia)e^{-t/T})$$


$$ln^{Im-Ia}= Im+Ie+Ia$$

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

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