# A little bit of help rearranging and equation

Hello,

Hopefully someone can help me rearrange this equation for x2.

The equation is

CB = Co e(-x2/4Dt)

It is changing the e into a log that is throwing me.

Thanks.

Seán

gb7nash
Homework Helper
In order to apply the log, you need to isolate the e(-x2/4Dt) term. How do you do that?

Hello.

Well, that would be

CB/Co = e(-x2/Dt)

gb7nash
Homework Helper
Ok, now log both sides. What do you get?

See, this is where im not sure.

Is it

ln(CB/Co) = ln(-x2/Dt)

?

gb7nash
Homework Helper
See, this is where im not sure.

Is it

ln(CB/Co) = ln(-x2/Dt)

?

The right-hand side is wrong. The left-hand side is fine. Take the ln of the right side, without trying to cancel anything out for now. What do we have?

So,

ln(CB/Co) = ln(e(-x2/Dt))

?

gb7nash
Homework Helper
That's fine. One well-known rule of ln is:

ln(ab) = b ln(a)

How can we apply this to the right-hand side?

Well, that would be

ln(CB/Co) = (-x2/Dt)ln(e)

and ln(e) is 1?

gb7nash
Homework Helper
Well, that would be

ln(CB/Co) = (-x2/Dt)ln(e)

and ln(e) is 1?

Correct. You can probably take it from here.

Yea, thats fantastic!

Many thanks!

Seán