You probably already know that the difference of squares $x^2-y^2$ can be factored as ($x+y)(x−y)$.
In a previous algebra class, you might have also encountered a formula to factor a difference of cubes: $x^3-y^3=(x^2+xy+y^2)(x-y)$.
Is there a way to factor $x^4 - y^4$? It turns out, there is:
$$ x^4 - y^4 = (x^3 + x^2y + xy^2 + y^3)(x-y) $$
There is also a way to factor $x^5 - y^5, x^6 - y^6$, etc. The general formula is:
$$ x^n - y^n = (x-y)\sum_{i=0}^{n-1}(x^{n-1-i}y^i) $$
This also gives us a formula for $\frac{x^n - y^n}{x-y}$:
$$ \frac{x^n - y^n}{x-y} = \sum_{i=0}^{n-1}(x^{n-1-i}y^i) $$
$$ \log_a(b) = \frac{\ln(b)}{\ln(a)} $$