Sequence convergence proof

Question

Sequence: $a_n=5r^{n-1}$ and $|r| \lt 1$

I am finding an $N$ for a convergence proof. My result is $$N \ge \frac{\ln\varepsilon/5}{\ln r} +1$$

And the textbook answer is $$ N \ge \frac{\ln 5/ \varepsilon}{\ln 1/r} +1 $$

Are these answers equivalent? If not, what is the problem?

Answer 1

Yes, $\log (1/x) = - \log x$. Use that in both the numerator and the denominator.