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 distance to …

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, I …

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 ...

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 versa. What's the in...

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 its own …

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 directly, it is …

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 it by itself n …

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 have such …

Sep 10, 2013 · We use multiplication for repeated addition, and in turn use exponents for repeated multiplication. What topic comes after this, for repeated exponentials? Is there something my …