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# Steps in an Equation watch

The following lines appear in an equation in the book: ln=natural log

-(L/R)ln(V-Ri) = t - (L/R)lnV

(L/R)ln(V/(V-Ri)) = t

V/(V-Ri) = e (to the power of Rt/L)

Can anyone explain the steps taken going from line 1 to 2 and 2 to 3.

If there's any missing lines, could you let me know. I can't seem to figure out how they've taken these steps.

Thank you!
2. (Original post by little pixie)

The following lines appear in an equation in the book: ln=natural log

-(L/R)ln(V-Ri) = t - (L/R)lnV

(L/R)ln(V/(V-Ri)) = t

V/(V-Ri) = e (to the power of Rt/L)

Can anyone explain the steps taken going from line 1 to 2 and 2 to 3.

If there's any missing lines, could you let me know. I can't seem to figure out how they've taken these steps.

Thank you!

Multiply both sides by R, divide by L:

Take exponentials of both sides

EDIT

and for step 1-2:

so

then factorise L/R

use that to get

3. From step 1 to 2. The log term is being brought from the right hand side to the left and a common factor of (L/R) is being take out of both log terms. Then by using the laws of logs: ln A - ln B = ln (A/B).

From step 2 to 3 (L/R) is being brought to the right hand side of the equation and then both sides are being raised as powers of e.

I hope you can follow this
4. (Original post by little pixie)

The following lines appear in an equation in the book: ln=natural log

-(L/R)ln(V-Ri) = t - (L/R)lnV

(L/R)ln(V/(V-Ri)) = t

V/(V-Ri) = e (to the power of Rt/L)

Can anyone explain the steps taken going from line 1 to 2 and 2 to 3.

If there's any missing lines, could you let me know. I can't seem to figure out how they've taken these steps.

Thank you!
From 1 to 2, they have added to both sides and recalled the law of logs which states that for use on the new LHS following the addition I mentioned.

From 2 to 3, they rearrange first for and then note that so they raised both sides as a power of e to get rid of the log.
5. Thanks very much guys. That's a great help. It looks a lot easier now once explained!
6. Re write

as

Factor out the -(L/R) on the left side to get

when you take the log of one thing away from the log of another thing it's the same as taking the log of their quotient. so....

getting closer now, lets add -(L/R) to both sides of the equation and raise e to the power of both sides of the equation the get rid of the natural logs.

Hope this helps you understand....Damn I hate LaTeX.
7. (Original post by little pixie)

The following lines appear in an equation in the book: ln=natural log

-(L/R)ln(V-Ri) = t - (L/R)lnV

(L/R)ln(V/(V-Ri)) = t

V/(V-Ri) = e (to the power of Rt/L)

Can anyone explain the steps taken going from line 1 to 2 and 2 to 3.

If there's any missing lines, could you let me know. I can't seem to figure out how they've taken these steps.

Thank you!
sorry double post[/edit]

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