Limit $\lim_{n→∞} [log(2+3^n)]/2n$ Find $\lim_{n→∞} [log(2+3^n)]/2n$
I have my work till the very last step then i dont know how to continue
$\lim_{n→∞} [log(2+3^n)]/2n$
=$\lim_{n→∞} log(3^n)+\lim_{n→∞} log[(2+3^n)/3n]$
=$\lim_{n→∞} log(3^n)+\lim_{n→∞} log[(2/3^n)+1/1]$
="I dont know what it is"$+1$
Since $\lim_{n→∞} log(3^n)$ is infinity???
What should I do?? Thanks!!

Hint: $\lim_{n\rightarrow \infty} \frac { \log (2+3^n)}{\log {3^n} } = 1$
Hint: $\frac {\log 3^n}{2n} = \frac {n \log 3}{2n} = \frac {\log 3}{2}$. Hence the limit (of this sequence to infinity) is $\frac {\log 3}{2}$.
