# How do I rearrange this physics equation?

How do I rearrange V = Voe^-(t/RC) for t?

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• To find t?

You can perform any operation as long as you do it to both sides of the equation. But if you "deconstruct" one side in the correct sequence you don't get into trouble.

According to SADMOB the first thing that we need to do is to get rid of multiplications and divisions.

divide both sides by Vo

V/Vo = e^(-t/RC)

The next step is to eliminate the function so that we can get to what is inside the brackets on the right

the inverse of "e to the power of" is the natural logarithm

ln( V/Vo) = - t/RC

the brackets on the left must be added to show that we are taking the ln of the entire side and the brackets on the right can be removed because there is nothing else left outside the brackets.

Now we wish to remove the division., The opposite is multiplication.

So multiply both sides by (RC)

(RC)* ln( V/Vo) = -t

Finally we wish to take the negative of both sides so that t is left on its own.

t = - (RC)* ln(V/Vo)

At each step the ORDER of the deconstruction is given by SADMOB.

The operation performed is always the inverse of whatever it is that needs to be removed.

This topic was some months of study at the year ten level.

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• Just take the logarithm on both sides.

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