- #1

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## Homework Statement

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

## Homework Equations

n/a

## The Attempt at a Solution

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

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