I don't understand point d)
What do you mean by efficient?
Any other literature you could reference? Cause this sounds interesting and I'd like to do some more research into this.
What do you mean by efficient?
Any other literature you could reference? Cause this sounds interesting and I'd like to do some more research into this.
By derivatives, that's minimized when B satisfies
0 = (log N) (1 / (log B) + B(-1/((log B)^2)(1/B)
==
0 = 1/(log B) - 1/(log B)^2
1 = log B
Base of the logarithm = B.
This looks like you can pick any logarithmic base b you want, and so any B you want, but in fact the derivative I wrote assumes e is the base (hence the term "natural" logarithm.
Other bases b would yield a scaling factor of ... e/b, since d(e^x)/dx = e^x
and b^x = e^((ln b) x)
You can chase "deeper" reasons for this all day long by digging deeper into the the many definitions/properties of e and proving they are equivalent.
Playing with e is the most fun you can have in pre/calculus.
The intuition is that (e) is the optimal water-level when limited water is distributed among a variable amount of buckets where all the filled buckets multiply each other. Alternatively, it's like how volume() is maximized where
volume(x, y, z) = (x y z)
const = (x + y + z)