I think I have finally come to terms with e, the base for the natural logarithm. It is a very useful thing. Looking through various help in math sites, I came across the below entry into the matter, to the effect that - historically - the invention of e became necessary in the on-going work in calculus as one tried to define integrations as the opposite of derivations ie that one could find the distance covered by a moving element as a non-constant speed by adding the little bits ie integration. Newton (1642-1726) does come before Euler (1707-1783)!
In effect, the fundamental theorem of calculus does posit that derivation and integration are opposites. The notion of primitive is a delicate one. one has to be aware of the difference between a free variable (for which one could sub a constant), a bound variable, and a silent one (place-holder), distinctions which came recently in mathematics.
If logarithms made calculations easy for times before the invention of the calculator, one can still appreciate it today as the bridge to those darn values that don't turn out evenly in calculation. Below,
e to power .25 does come back to itself if the value is multiplied by itself three times!!
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