Mar 8, 2014 · Exponentiation is a correspondence between addition and multiplication. Think of a number line, with $0$ in the "middle", and tick marks at each integer. Moving a certain …

Dec 18, 2023 · I was wondering why addition has one inverse (subtraction), multiplication has one inverse (division), but exponentiation has two (radication and logarithm). After a bit of thinking, …

Oct 3, 2014 · You know, like addition is the inverse operation of subtraction, vice versa, multiplication is the inverse of division, vice versa , square is the inverse of square root, vice …

Jun 21, 2021 · I also would like to know who defined exponentiation for these cases and in which paper. --- FYI, elementary things like this from well before the last hundred years or so often …

Apr 25, 2017 · The definition of the exponential with integer exponents is straightforward to define: $x^n=\underbrace {x\cdot\ldots\cdot x}_ {n-\text {times}}$. These days I've ...

May 21, 2018 · When rigorously laying out foundations of all of analysis, the usual method is to use the definition $$ a^b = \exp (b \log (a)) $$ While you could try and define exponentiation …

I saw here in math.stackexchange some proofs of how the log and exp functions are related to each other, but I want to get an intuition for that. In layman terms, how would you explain the …

Take the following: (2)^3 = 8 I understand that this is 2 * 2 * 2 = 8 My question is how do I reverse engineer this if I do not know the power like this: (2)^x = 8 What is the value of x? x could

Nov 3, 2017 · Rather than trying to press complex exponentiation into the mold of repeated multiplication, see complex exponentiation -- or more fundamentally, the function $\exp$ -- as …

Oct 7, 2016 · We can define exponentiation as repeated multiplication and solve the problem of "what is the nth root of something" by defining it as "it's whatever thing that, when you multiply …