Solve the equation: $p = 1+r+r^2+ \ldots+r^n$

Question

There is an equation: $p = 1+r+r^2+ \ldots+r^n$.

The right side of this equation can reduce to $(r^n-1)/(r-1)$, but I cannot find the way to find a function of $r$ and $p$ such that $n = f(p, r)$, can someone know how to get this function.

Answer 1

$$p= \frac{r^n-1}{r-1}$$ $$r^n = p(r-1)+1$$

$$n = \frac{\ln (p(r-1)+1))}{\ln r}$$