How can I calculate $\lim\limits_{n \to \infty} \frac{\log_{a} n}{\log_{b} n}$. Where $a$ and $b$ are two integers.
How can I calculate limit of division of two logarithms
0
$\begingroup$
limits
logarithms
-
4Hint: the elements of the sequence do not actually de$p$e$n$d o$n$ $n$... – 2011-10-07
2 Answers
3
Note that $\frac{\log_a(n)}{\log_b(n)}=\log_a(b)$ (see here).
1
$\lim\limits_{n \to \infty} \frac{\log_{a} n}{\log_{b} n}$, Now,if we change bases to e we get following expressions:
$\lim\limits_{n \to \infty}\frac{\ln n/\ln a}{\ln n/ \ln b} =\lim\limits_{n \to \infty} \frac{\ln b}{\ln a}=\frac{\ln b}{\ln a} $