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

AI Thread Summary
The discussion centers on the relationship between the exponential function and the natural logarithm, specifically why e^-1 is considered the inverse of the natural logarithm. It clarifies that if y = ln(x), then x = e^y, establishing the inverse relationship. The mention of charging and discharging capacitors highlights the use of e^-1 in equations like Q=Qmax(1-e^-1), which relates to exponential decay. The term e^-1 can be interpreted as 1/e, reinforcing the concept of inverse in the context of natural logarithms. Understanding this relationship is crucial in applications involving exponential growth and decay.
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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