why is the addition of same-base logarithms the same as the multiplication of same-base logarithms, and same for subtracting and dividing same-base logs?

Question

I know it’s because of the “product property” but that doesn’t explain the inner workings for me and the proof is bouncing right off my skull.

In: Mathematics

Answer 1

A logarithm is the inverse of n^x. So logn(n^x) = x. Kinda like how multiplication and division are inverses or addition and subtraction are inverses. So n^x and logn(x) follow the same rules.