# Is there a limit theorem for this?

## Homework Statement

The problem is much bigger, but part of the proof I've written hinges on the assumption that for $$a \in \mathbb{R}, x_n$$ converging to $$x, a^{x_n}$$ converges to $$a^x$$

n/a

## The Attempt at a Solution

I have tried taking $$\log_a$$ of both sides but that only circumvents the problem, I now have to show that $$\log_a x_n$$ converges to $$\log_a x$$

edit: I see now I can use the fact that log is continuous to show what I need. Please lock.