Why is e^-1 considered the inverse of the natural logarithm?

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Discussion Overview

The discussion revolves around the relationship between the exponential function and the natural logarithm, specifically addressing why e^-1 is considered the inverse of the natural logarithm. The context includes mathematical reasoning and its application in the charging and discharging of capacitors.

Discussion Character

  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant questions the relationship by stating that if y = ln(x), then x = ey, using e as the base of the natural logarithm.
  • Another participant references a section on charging/discharging capacitors, noting that the charge equation includes e^-1, which they interpret as the inverse of the natural logarithm.
  • There is a suggestion that e^-1 could mean "the inverse of the basis of the natural log, e," with the clarification that e^-1 equals 1/e.
  • A later reply expresses agreement with the interpretation of e^-1 as the inverse of e, indicating a shared understanding among some participants.

Areas of Agreement / Disagreement

Participants express varying interpretations of the relationship between e^-1 and the natural logarithm, with some agreeing on the interpretation while others raise questions about the clarity of the original question. The discussion does not reach a definitive consensus.

Contextual Notes

The discussion includes assumptions about the definitions of inverse functions and the context of their application in capacitor equations, which may not be fully resolved.

Bengo
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Why is e^-1 the inverse of natural log e? Thank you
 
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Your question is confusing. Let y = ln(x), then x = ey. If x = e, y = 1.
 
Well I was reading a section on charging/ discharging capacitors and this is what it said: charge on a capacitor builds up on the capacitors plates exponentially, indicated in the passage by the repeated appearance in the charge equation of e^-1, the inverse of the natural log e. And I think the equation they are referring to is Q=Qmax(1- e^-1).
 
Could it mean "the inverse of the [basis of the] natural log[,] e"? As e-1 = 1/e
 
mfb said:
Could it mean "the inverse of the [basis of the] natural log[,] e"? As e-1 = 1/e


Ok I'll go with that because it's what I was thinking too. Thank you!
 

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