The discussion revolves around rearranging an exponential equation to solve for the variable λ. The context involves understanding the relationship between pressure ratios and a distance variable in a scientific formula.
Some participants express confidence in their rearrangement attempts, while others question their understanding of differentiation and the correct setup of the equation. There is acknowledgment of potential errors in variable placement, but no consensus on the correctness of the approach has been reached.
Participants note confusion regarding the differentiation process and the arrangement of the pressure variables, indicating a need for clarification on these points.
annalise17 said: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...
annalise17 said: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.