Math Problem Issue: Deriving 4.12 from 4.11

  • Thread starter Thread starter matt222
  • Start date Start date
Click For Summary
SUMMARY

The discussion centers on the derivation of equation 4.12 from equation 4.11 in a mathematical context. The user questions the validity of the book's output, suggesting that the correct expression should be (n-N)/n instead of (N-n)/n. Furthermore, the user expresses confusion regarding the sign change when transitioning from 4.11 to 4.12, particularly under the assumption that N is significantly greater than n (N>>n). The user ultimately seeks clarification on these derivations and their implications.

PREREQUISITES
  • Understanding of logarithmic functions and their properties
  • Familiarity with mathematical derivations and manipulations
  • Knowledge of the context and implications of equations in mathematical texts
  • Ability to analyze and critique mathematical proofs
NEXT STEPS
  • Review the derivation process of logarithmic equations in advanced mathematics
  • Study the implications of limits and assumptions in mathematical proofs
  • Examine the properties of natural logarithms, particularly regarding negative arguments
  • Explore the significance of asymptotic notation in mathematical analysis
USEFUL FOR

Students studying advanced mathematics, educators teaching calculus or algebra, and anyone involved in mathematical proof analysis.

matt222
Messages
130
Reaction score
0

Homework Statement



It is not a homework but I will call it an homework for me, the problem for math derivation shown in the attached file, it is from the book I use. From equastion 4.11 we have to derive 4.12, in this step i disagree with output result since it should be (n-N/n) not as the book state (N-n/n)? does anyone agree or disagree with this first step?

second thing if we made our answer which is n-N/n is the correct one do you agree that the final output of 4.14 is correct once the assumption made N>>n! in this case I disagree with my answer and agree with the book answer but now how and why he flip the sign once he jump from 4.11 to 4.12 it doesn't make sense!

any help

Homework Equations





The Attempt at a Solution

 

Attachments

  • llll.jpg
    llll.jpg
    31.9 KB · Views: 482
Physics news on Phys.org
In equation 4.11, it looks like the argument of ln should be N-n, not n-N. Since n<N, ln (n-N) would be undefined.
 

Similar threads

Master equation -> diffusion equation
  • · Replies 3 ·
Replies
3
Views
3K
Deriving MTW's Equation 21.90 from Equation 21.83
  • · Replies 1 ·
Replies
1
Views
2K
Deriving conjugate momenta from the Einstein-Hilbert density
  • · Replies 1 ·
Replies
1
Views
2K
Calculating specific heat capacity from entropy
  • · Replies 1 ·
Replies
1
Views
2K
Understanding Green's second identity and the reciprocity theorem
  • · Replies 3 ·
Replies
3
Views
6K
Zangwill, problem 10.19 - A Matching condition for the vector potential A
  • · Replies 1 ·
Replies
1
Views
2K
Thermodynamics equilibrium with respect to matter flow
  • · Replies 1 ·
Replies
1
Views
2K
Debugging a Backprop Neural Network: Issues & Solutions
  • · Replies 3 ·
Replies
3
Views
2K
Quick derivation question Quantum Mechanics
  • · Replies 2 ·
Replies
2
Views
1K
Equation of motion from a Lagrangian
  • · Replies 5 ·
Replies
5
Views
2K