Finding λ in an Exponential Equation: A Scientific Approach

[annalise17]

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...

 

[Bread18]

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?
\frac{P_1}{P_2}=e^{-\frac{(Z_2 - Z_1)}{\lambda}}

Also, what are you differentiating?

 

[annalise17]

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.

 

[Bread18]

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 P_1 and P_2 mixed up :P) Then that is right.