Relation of Energy Fluxes of Two Objects

[Airsteve0]

Homework Statement

Suppose two objects have energy fluxes, f and f + Δ
f, where

Δf ≪ f. Derive an approximate expression for the magnitude difference

Δm between these objects. Your expression should have Δ
m
proportional to
Δf.

Homework Equations

Δm = m2 - m1 = 2.5 * log(f1/f2)

The Attempt at a Solution

So the issue is that I'm not sure which of these solutions would be the better one to work with. However, I did make an approximation with the one as shown below and I'm not sure if it is quite accurate enough. Any assistance is greatly appreciated.

ARRANGEMENT 1: Δm = 2.5 * log(f / f+Δf) = 2.5 * [ log(f) - log (f + Δf)]

or,

ARRANGEMENT 2: Δm = 2.5 * log(f+Δf / f) = 2.5 * log(1 + Δf/f) ≈ 2.5*Δf

The second arrangement seems more correct to me but I would feel more confident with a second opinion.

 

[Airsteve0]

the reason I have two arrangements is that the question is quite open-ended as to which object has which flux