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

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 connect...

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 …

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 …

Nov 3, 2017 · I don't think you can intuitively understand complex exponentiation as a generalization of real exponentiation without first synthesizing an understanding of exponentiation.

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 …