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The natural base, e, 2.718281828..., was selected because the derivatived/dx ex is equal to x. This simplifies many calculations, derivatives, integrals, etc.

Additional:

This base is used because there is a series (of terms) for powers of (e), therefore, powers of any value can be found just by plugging in values in the series.

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Q: Why use a natural base logarithm?
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