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

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SUMMARY

e^-1 is recognized as the inverse of the natural logarithm due to the relationship defined by the equation y = ln(x), which leads to x = e^y. In the context of capacitor charging and discharging, the equation Q = Qmax(1 - e^-1) illustrates the exponential decay of charge, where e^-1 represents the inverse of the base of the natural logarithm, e. This confirms that e^-1 is equivalent to 1/e, reinforcing its role as the inverse in logarithmic functions.

PREREQUISITES
  • Understanding of natural logarithms and their properties
  • Familiarity with exponential functions
  • Basic knowledge of capacitor charging and discharging equations
  • Concept of inverse functions in mathematics
NEXT STEPS
  • Study the properties of natural logarithms and their inverses
  • Explore exponential decay in electrical engineering contexts
  • Learn about capacitor charge equations and their applications
  • Investigate the mathematical relationship between e and logarithmic functions
USEFUL FOR

Students in mathematics or electrical engineering, educators explaining logarithmic functions, and professionals working with capacitor circuits will benefit from this discussion.

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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