Struggling to understand how I get this answer

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Discussion Overview

The discussion revolves around understanding a mathematical expression involving integration and logarithmic functions. Participants are examining the calculation of an integral with limits and how it relates to the natural logarithm, specifically in the context of a university paper example.

Discussion Character

  • Mathematical reasoning
  • Homework-related

Main Points Raised

  • One participant expresses confusion about how to arrive at the answer of ln(2) from the integral W = 220∫ V^-1 dV between the limits of 0.1 and 0.2.
  • Another participant confirms that the difference of the logarithms, ln(0.2) - ln(0.1), simplifies to ln(0.2/0.1) which equals ln(2).
  • Several participants provide the numerical values of ln(0.2) and ln(0.1) to illustrate the calculation, showing that the difference indeed results in ln(2).
  • Participants acknowledge the clarity gained from the discussion, indicating a shared understanding of the logarithmic properties involved.

Areas of Agreement / Disagreement

Participants generally agree on the mathematical steps leading to the conclusion that ln(0.2) - ln(0.1) equals ln(2). However, initial confusion about the process is evident, suggesting that while the final result is accepted, the path to understanding it was not straightforward for all.

Contextual Notes

The discussion does not address potential assumptions about the integration process or the context of the problem, which may affect the interpretation of the integral and its limits.

PizzaWizza
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Struggling to understand how this answer works.
This is just a worked example from a university paper.

W = 220∫ V^-1 dV...between the limits of 0.1 & 0.2...(Answer is 152.49 Rad)

I understand that the basic rule for a negative power would give us ln x, but from here I would say that the answer would be the difference of ln 0.2 and ln 0.1?
I need to get ln(2) for the answer to be correct, just not sure how?
 
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Surely ln(0.2) - ln(0.1) = ln(0.2/0.1) = ln(2)
 
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Merlin3189 said:
Surely ln(0.2) - ln(0.1) = ln(0.2/0.1) = ln(2)
I was deducting ln 0.1 from ln 0.2, thanks
 
PizzaWizza said:
I was deducting ln 0.1 from ln 0.2, thanks
Same difference:

ln (0.2) = -1.6094
ln (0.1) = -2.3026

ln (0.2) - ln (0.1) = -1.6094 - (-2.3026) = 0.6931 = ln (2)
 
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SteamKing said:
Same difference:

ln (0.2) = -1.6094
ln (0.1) = -2.3026

ln (0.2) - ln (0.1) = -1.6094 - (-2.3026) = 0.6931 = ln (2)
Ah. I see. That makes it clearer. Thanks
 

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