Many of the equations are hard to type, so I will stick with the ‘^’ notation. i.e. 3^5 is 3 to the power of 5, or 243. There are other notations to be addressed later. (Perhaps next class) I will start by addressing WHY the power operation have TWO inverse operations. Why is there only ONE inverse operation for multiplication. The answer is easy: there is no commutative law in powers. 35=53, right? But the same doesn’t hold for powers. So there are two inverse operations: One, where you know the base. Two, where you know the exponent. The second one is easier, so we will start with it.
You know a^b, b, and you want to know a. The simple answer is that (a^b)^(b/1)=a
A simple power rule yields WHY. (a^b)^(b/1)=a^(b*b/1)=a^1=a [Of course b can’t be 0 or we are doomed.]
A more interesting question is about the first case, where you know the base.
Sadly, this ended up being ANOTHER OPERATION, the logarithm. They don’t teach logarithm in middle school. But logarithm is one of the best inventions in math. Suppose you want to bash some multiplication, but you only want to do addition. You only need a logarithm sheet WITH ANY BASE (as long as it is not 1), and you can do it easily.
Why? This is one of the very interesting problems, leading to a logarithm rule. How? This also have links with the logarithm rule. In fact, not only can you calculate multiplication with addition, you can calculate powers with multiplication, which means using it all AGAIN will calculate powers with addition.
Why it works depend heavily upon power rules, so we encourage you to learn it.
The next lesson is on to my book Math for Dummies, here: Math for Dummies. You may ask me with my email. The following link zooms you to my email.
https://www.notion.so/numberbasher/Inverse-of-the-Power-68074b8809724c299cf456942b46b018#f4175efa0c1e4753a9d884fcc95a762c
Thank you for reading this. If you have any problem regarding THIS ARTICLE or anything else (that has to do with math), feel free to ask me.
Response guaranteed in two weeks.
Email: [email protected]
Back: