Rearranging CB = Co e(-x2/4Dt) for x2

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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
 

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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)
 
Ok, now log both sides. What do you get?
 
See, this is where I am not sure.

Is it

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

?
 
SMOF said:
See, this is where I am 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))

?
 
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?
 
SMOF said:
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, that's fantastic!

Many thanks!

Seán