Rearranging and Exponentials

  • Thread starter annalise17
  • Start date
  • #1
10
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Homework Statement


I believe I need to rearrange this formula to find an equation for λ:

P2 / P1 = exp( - (z2 - z1)) / λ




Homework Equations


I think I need to differentiate and find the natural log of both sides then rearrange


The Attempt at a Solution


Differentiate to: ln(P2 / P1) = ( - (z2 - z1) / λ

Rearrange to: λ = - Δz / ln(P2 / P1)

Does that look right? I appear to be able to calculate it....
 

Answers and Replies

  • #2
100
0

Homework Statement


I believe I need to rearrange this formula to find an equation for λ:

P2 / P1 = exp( - (z2 - z1)) / λ




Homework Equations


I think I need to differentiate and find the natural log of both sides then rearrange


The Attempt at a Solution


Differentiate to: ln(P2 / P1) = ( - (z2 - z1) / λ

Rearrange to: λ = - Δz / ln(P2 / P1)

Does that look right? I appear to be able to calculate it....
Is this what you're meant to rearrange?
[tex]\frac{P_1}{P_2}=e^{-\frac{(Z_2 - Z_1)}{\lambda}}[/tex]

Also, what are you differentiating?
 
  • #3
10
0
Hmm I may not be differentiating anything actually! Sorry, my maths is lacking quite a bit so I mix up my terminology. But yes, that looks right (although I have P1 and P2 the other way around, I'll check that) I didn't know how to input it on here so attempted it in linear form.
 
  • #4
100
0
Hmm I may not be differentiating anything actually! Sorry, my maths is lacking quite a bit so I mix up my terminology. But yes, that looks right (although I have P1 and P2 the other way around, I'll check that) I didn't know how to input it on here so attempted it in linear form.
Well if that's what you were asked to rearrange (Yes I got the [itex]P_1[/itex] and [itex]P_2[/itex] mixed up :P) Then that is right.
 

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