Is there a limit theorem for this?

  • #1

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.
 

Answers and Replies

Related Threads on Is there a limit theorem for this?

Replies
1
Views
5K
Replies
1
Views
3K
Replies
8
Views
871
Replies
6
Views
1K
Replies
5
Views
717
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
0
Views
1K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
7
Views
6K
  • Last Post
Replies
2
Views
1K
Top