What is it about the number e that makes it so that taking log to the base e is called the natural logarithm?
In: Mathematics
Short answer is that’s just a name. There’s nothing special mathematically about the name aside from a feeling.
Long answer is, there are often things in math we call canonical or natural. These are somehow special in some fundamental way. e is one such number. Consider the following functional form:
y = a^x
If you take the derivative of this, you get y’ = ln(a) a^x . Seems a bit complicated doesn’t it? But if your base were e instead of a, then you’d get y is its own derivative. In fact e shows up in seemingly different and unrelated fields in a similar way. This makes mathematicians feel there’s something special about e.
Given that ln is e’s inverse, it therefore gets the honorific of “natural” log.
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