I was wondering about the convergence of a sequence based on the convergence of the logarithm of the sequence. I can't seem to find anything online, and it seems to make intuitive sense, but I'm not entirely sure and am finding it difficult to show it.
To state the issue, if we have $\log(a_n)$ converges, can it be shown that $a_n$ likewise converges to the value of $e$ raised to the limit?
Again, this seems somewhat intuitive, but I can't seem to figure out how to prove it effectively or find anything online. Any help would be appreciated.
Hint: $\exp$ is a continuous function.